Development of an Open Source Software Tool for Propeller Design in the MAAT Project

Transcription

1 UNIVERSIDADE DA BEIRA INTERIOR Engenharia Development of an Open Source Software Tool for Propeller Design in the MAAT Project Desenvolvimento de uma Ferramenta Computacional de Código Aberto para Projeto de Hélices no Âmbito do Projeto MAAT João Paulo Salgueiro Morgado Tese para obtenção do Grau de Doutor em Engenharia Aeronáutica (3º ciclo de estudos) Orientador: Prof. Doutor Miguel Ângelo Rodrigues Silvestre Coorientador: Prof. Doutor José Carlos Páscoa Marques Covilhã, março de 2016

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5 Aos meus pais e às minhas irmãs v

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7 Agradecimentos A execução deste trabalho só foi possível devido à colaboração, disponibilidade e empenho de algumas pessoas às quais quero desde já manifestar o meu mais sincero agradecimento. Ao Professor Miguel Silvestre, pela orientação neste trabalho, pelos conhecimentos que me transmitiu, pelo rigor científico com que sempre desenvolveu o trabalho e por me ter incutido um espírito crítico. Agradeço-lhe também pela sua amizade, por toda a disponibilidade e atenção que sempre dispensou ao longo destes anos. Ao Professor José Páscoa, pela sua co-orientação neste trabalho, pela sua constante disponibilidade, pelos conhecimentos que me transmitiu e pelos conselhos que me deu. Quero ainda agradecer-lhe o espaço que me disponibilizou no ClusterDEM, permitindo que este trabalho fosse desenvolvido num ambiente calmo e confortável. Ao Sr. Rui, ao Pedro Santos e ao Pedro Alves pelo apoio prestado na parte experimental deste trabalho e pelo seu empenho na resolução dos problemas que foram surgindo. Ao Carlos, à Galina, ao Shyam, ao Jakson e ao Frederico, com quem partilhei o espaço de trabalho do ClusterDEM, pela disponibilidade sempre demonstrada e ainda pela possibilidade de ter partilhado estes anos com pessoas de diferentes culturas e costumes. Ao Amilcar, ao Rui, ao Mahdi e ao Luís por tudo o que partilhámos ao longo destes anos, pelo apoio que sempre me deram nos momentos menos bons, pelas discussões mais ou menos científicas que tivemos e sobretudo pela vossa amizade. A ti, Andreia, por tudo. Por me fazeres sorrir, por estares sempre a meu lado por me aturares e por me ajudares a ver sempre o lado mais positivo das coisas. O meu obrigado não é suficiente por todo o carinho que demonstras por mim. À minha Mãe, ao meu Pai e às minhas Irmãs pois sem vocês nada disto teria sido possivel. Obrigado por estarem sempre presentes, pela compreensão, pelo constante apoio e pelo encorajamento ao longo destes anos. Não é possível agradecer tudo o que fazem por mim. A todos o meu Muito Obrigado! Support The present work was performed as part of Project MAAT (Ref. No ) supported by European Union Seventh Framework Programme. Part of the work was also supported by C-MAST Center for Mechanical and Aerospace Sciences and Technologies, Portuguese Foundation for Science and Technology Research Unit No vii

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9 Resumo Nesta tese é apresentado o desenvolvimento de um novo código para projeto e análise de hélices, capaz de prever adequadamente o desempenho a baixos números de Reynolds. O JBLADE foi desenvolvido partindo dos códigos QBLADE e XFLR5 e utiliza uma versão aperfeiçoada da teria do elemento da pá que contém um novo modelo que considera o equilíbrio tridimensional do escoamento. O código permite que a pá seja introduza como um número arbitrário de secções, caracterizadas pela sua posição radial, corda, ângulo de incidência, comprimento, perfil e ainda pela polar 360º associada ao perfil. O código permite uma visualização gráfica em 3D da pá, ajudando o utilizador a detetar possíveis inconsistências. O JBLADE também permite uma visualização direta dos resultados das simulações através de um interface gráfico, tornado o código acessível e de fácil compreensão. Além disso, a interligação entre os diferentes módulos do JBLADE evita operações demoradas de importação e exportação de dados, diminuindo assim possíveis erros criados pelo utilizador. O código foi desenvolvido como um código aberto, para a simulação de hélices, e que tem a capacidade de estimar o desempenho de uma determinada geometria de hélice nas condições de operação do seu ponto de projeto e fora do seu ponto de projeto. O trabalho de desenvolvimento aqui apresentado foi focado no projeto de hélices para dirigíveis de grande altitude no âmbito do projeto MAAT (Multibody Advanced Airship for Transportation). O software foi validado para diferentes tipos de hélice, provando que pode ser utilizado para projetar e otimizar hélices para diferentes finalidades. São apresentadas a derivação e validação do novo modelo de equilíbrio tridimensional do escoamento. Este modelo de equilíbrio 3D tem em conta o possível movimento radial do escoamento ao longo do disco da hélice, melhorando as estimativas de desempenho do software. O desenvolvimento de um novo método para a estimativa do coeficiente de arrasto dos perfis a 90º, permitindo uma melhor modelação do desempenho pós-perda é também apresentado. Diferentes modelos de pós perda presentes na literatura e originalmente desenvolvidos para a indústria das turbinas eólicas foram implementados no JBLADE e a sua aplicação a hélices para melhorar a estimativa do desempenho foi analisada. Os resultados preliminares mostraram que a estimativa de desempenho das hélices pode ser melhorada, utilizando estes modelos de pós-perda. Uma metodologia de projeto inverso, baseada no mínimo das perdas induzidas foi implementado no JBLADE, de modo a ser possível obter hélices com geometrias otimizadas para um dado ponto de projeto. Além disto, um módulo de cálculo estrutural foi também implementado, permitindo estimar o peso das pás, a deformação das mesmas, quer em termos de flexão, quer em termos de torção, devido à tração gerada pela própria hélice e aos momentos do perfil. Para validar as estimativas de desempenho do JBLADE foram utilizadas hélices originalmente apresentadas nos relatórios técnicos NACA, nomeadamente no relatório técnico 594 e 530. Estas hélices foram simuladas no JBLADE e os resultados foram comparados com os dados experimentais e com as estimativas de desempenho ix

10 obtidas através de outros códigos numéricos. O módulo de projeto inverso e o módulo estrutural foram também validados, através da comparação com outros resultados numéricos. De modo a verificar a fiabilidade do código XFOIL usado no JBLADE para previsão das características dos perfis das pás, o modelo de turbulência k-ω Shear Stress Transport e uma versão reformulada do modelo de transição k-kl-ω foram utilizados em simulações RANS para comparação dos resultados do desempenho aerodinâmico de perfis. Os resultados mostraram que o código XFOIL dá uma estimativa de desempenho mais próxima dos dados obtidos experimentalmente do que os modelos RANS CFD, provando que pode ser utilizado no JBLADE como ferramenta de estimava de desempenho aerodinâmico dos perfis. Em vez da tradicional prescrição do coeficiente de sustentação ao longo da pá para melhor L/D, foi utilizado os pontos de melhor L 3/2 /D para o projeto de uma hélice para o dirigível cruzador do projeto MAAT. Os procedimentos de otimização empregados ao longo do processo de projeto destas hélices para utilização em grandes altitudes são também descritos. As hélices projetadas com o JBLADE foram analisadas e os resultados obtidos foram comparados com simulações convencionais de dinâmica de fluidos computacional, uma vez que não existem dados experimentais para estas geometrias em particular. Foram utilizadas duas aproximações diferentes de modo a obter duas geometrias finais. Foi mostrado que esta nova abordagem de projeto de hélices leva à minimização da corda necessária ao longo da pá, enquanto a tração e a eficiência da hélice são maximizadas. Foi desenvolvida uma nova instalação experimental para ensaio e caracterização de hélices de baixo número de Reynolds no âmbito do projeto MAAT, que foi posteriormente utilizada para desenvolver e validar ferramentas numéricas para projeto destas hélices. Além da descrição do desenvolvimento da instalação experimental, é também apresentada a validação da mesma, através da comparação das medições de diferentes hélices com dados experimentais presentes na literatura, obtidos em diferentes instalações de referência. Foi construída e testada uma réplica da hélice APC 10 x7 SF, fornecendo dados adicionais para a validação do JBLADE. É ainda apresentado o processo de desenho da réplica no software CAD e de construção dos moldes e do protótipo da hélice. Os resultados mostraram uma boa concordância entre as estimativas do JBLADE e as medições experimentais. Assim, conclui-se que o JBLADE pode ser utilizado para projetar e estimar o desempenho das hélices que poderão ser utilizadas pelo dirigível cruzador do MAAT bem como em outras aplicações. Palavras-chave JBLADE Software, Teoria do Elemento de Pá, Correções Pós-Perda, Equilíbrio 3D do escoamento, Projeto Inverso de Hélices, Simulação de Hélices em Dinâmica de Fluidos Computacional, Testes de Hélices em Túnel de Vento. x

11 Abstract This thesis presents the development of a new propeller design and analysis software capable of adequately predicting the low Reynolds number performance. JBLADE software was developed from QBLADE and XFLR5 and it uses an improved version of Blade Element Momentum (BEM) theory that embeds a new model for the three-dimensional flow equilibrium. The software allows the introduction of the blade geometry as an arbitrary number of sections characterized by their radial position, chord, twist, length, airfoil and associated complete 360º angle of attack range airfoil polar. The code provides a 3D graphical view of the blade, helping the user to detect inconsistencies. JBLADE also allows a direct visualization of simulation results through a graphical user interface making the software accessible and easy to understand. In addition, the coupling between different JBLADE modules avoids time consuming operations of importing/exporting data, decreasing possible mistakes created by the user. The software is developed as an open-source tool for the simulation of propellers and it has the capability of estimating the performance of a given propeller geometry in design and off-design operating conditions. The current development work was focused in the design of airship propellers. The software was validated against different propeller types proving that it can be used to design and optimize propellers for distinct applications. The derivation and validation of the new 3D flow equilibrium formulation are presented. This 3D flow equilibrium model accounts for the possible radial movement of the flow across the propeller disk, improving the performance prediction of the software. The development of a new method for the prediction of the airfoil drag coefficient at a 90 degrees angle of attack for a better post-stall modelling is also presented. Different post-stall methods available in the literature, originally developed for wind turbine industry, were extended for propeller analysis and implemented in JBLADE. The preliminary analysis of the results shows that the propeller performance prediction can be improved using these implemented post-stall methods. An inverse design methodology, based on minimum induced losses was implemented in JBLADE software in order to obtain optimized geometries for a given operating point. In addition a structural sub-module was also integrated in the software allowing the estimation of blade weight as well as tip displacement and twist angle changes due to the thrust generation and airfoil pitching moments. To validate the performance estimation of JBLADE software, the propellers from NACA Technical Report 530 and NACA Technical Report 594 were simulated and the results were checked against the experimental data and against those of other available codes. The inverse design and structural sub-module were also validated against other numerical results. To verify the reliability of XFOIL, the XFOIL Code, the Shear Stress Transport k-ω turbulence model and a refurbished version of k-kl-ω transition model were used to estimate the airfoil aerodynamic performance. It has been shown that the XFOIL code gives the closest prediction xi

12 when compared with experimental data, providing that it is suitable to be used in JBLADE Software as airfoil s performance estimation tool. Two different propellers to use on the MAAT high altitude cruiser airship were designed and analysed. In addition, the design procedure and the optimization steps of the new propellers to use at such high altitudes are also presented. The propellers designed with JBLADE are then analysed and the results are compared with conventional CFD results since there is no experimental data for these particular geometries. Two different approaches were used to obtain the final geometries of the propellers, since, instead of using the traditional lift coefficient prescription along the blade, the airfoil s best L 3/2 /D and best L/D were used to produce different geometries. It was shown that this new first design approach allows the minimization of the chord along the blade, while the thrust and propulsive efficiency are maximized. A new test rig was developed and used to adequately develop and validate numerical design tools for the low Reynolds numbers propellers. The development of an experimental setup for wind tunnel propeller testing is described and the measurements with the new test rig were validated against reference data. Additionally, performance data for propellers that are not characterized in the existing literature were obtained. An APC 10 x7 SF replica propeller was built and tested, providing complementary data for JBLADE validation. The CAD design process as well as moulds and propeller manufacture are also described. The results show good agreement between JBLADE and experimental performance measurements. Thus it was concluded that JBLADE can be used to design and calculate the performance of the MAAT project high altitude cruiser airship propellers. Keywords JBLADE Software, Blade Element Momentum Theory, Post-Stall Corrections, 3D Flow Equilibrium, Propeller Inverse Design, CFD Propeller Simulation, Wind Tunnel Testing xii

13 Resumo Alargado Este trabalho apresenta o desenvolvimento de um nova ferramenta para projeto e análise do desempenho de hélices operando a baixos números de Reynolds. A ferramente desenvolvida é um software que contém uma interface gráfica e que foi desenvolvido tendo como base os softwares QBLADE e XFLR5, já existentes. A inovação deste código consiste na implementação de uma versão melhorada da teoria do elemento de pá, normalmente utilizada por outros códigos de projeto e análise de desempenho de hélices, que tem em conta um equilíbrio tridimensional do escoamento, contabilizando assim a rotação da esteira, e melhorando as previsões de desempenho das hélices. Este trabalho foi desenvolvido no âmbito do projeto europeu Multibody Advanced Airship for Transport (MAAT), que envolveu mais de 15 entidades, e que pretende implementar um novo modelo de transporte através da utilização de dirigíveis. Neste modelo são utilizados 2 tipos de dirigíveis: um crusador, que operará entre os m de altitude e um outro tipo de dirigivel que será responsável por fazer a ligação entre o solo e o crusador. Ora, como apresentado ao longo do documento, as hélices têm vindo a ser utilizadas em veículos com uma altitude de operação semelhante, pelo que é essencial o desenvolvimento de uma ferramenta fiável para projectar e analisar as hélices do crusador do projeto MAAT. Durante o estudo e análise do estado atual das teorias aplicavéis a hélices, chegou-se à conclusão que era possível melhorar essas teorias. Este modelo de equilíbrio tri-dimensional tem em conta o possível movimento radial do escoamento ao longo do disco da hélice, melhorando as estimativas de desempenho do software Além disto, como as hélices têm ângulos de torção bastante elevados, principalmente na zona da raíz, os perfis das pás estão muitas vezes a operar em regime pós-perda, e os códigos númericos utilizados para prever o seu desempenho nem sempre fornecem dados fidedignos acerca do desempenho dos mesmos. O JBLADE utiliza um método que consiste na extrapolação dos valores do coeficiente de sustentação e do coeficiente de arrasto apresentado na literatura. Neste modelo, a previsão do valor do coeficiente de arrasto tem uma importância vital para uma correcta extrapolação deste mesmo coefficiente, podendo levar a diferenças significativas na previsão de desempenho da hélice. Assim, de modo a melhorar a previsão de desempenho da hélice foi desenvolvido um novo método para estimar o coeficiente de arrasto de um perfil a um angulo de ataque de 90º. Este método baseia-se no raio do bordo de ataque do perfil e foi também incorporado no JBLADE. Foram também implementados no JBLADE diferentes modelos de pós perda, originalmente desenvolvidos para a indústria de turbinas eólicas que como demonstrados, melhoram a previsão de desempenho para baixas razões de avanço. Foram comparados diferentes modelos e os resultados foram analisados e discutidos. Estes modelos estão disponíveis no JBLADE, podendo ser utilizados ou não na simulação da hélice, conforme as preferências do utilizador. xiii

14 De formar a agilizar o processo de projeto de uma hélice, foi implementado um método de projeto inverso descrito na literatura. Foram feitas algumas modificações ao método original, nomeadamente através da utilização do ponto de melhor L/D e L 3/2 /D dos perfis, permitindo que a corda necessária para produzir uma determinada tração seja menor. Este processo foi validado através da comparação dos dados obtidos no JBLADE com outros dados disponíveis na literatura bem como com outros códigos disponíveis. Esta implementação do método de projeto inverso foi depois utilizado para projetar uma hélice para aplicação no dirigível crusador do projeto MAAT. Uma vez que as hélices que serão utilizadas no dirigível do projeto MAAT serão bastante grandes, é importante assegurar que não sofrerão uma deformação excessiva, que poderá levar à sua destruição. Assim, foi implementado um módulo de cálculo estrutural, no qual a pá da hélice é considerada uma viga encastrada. Esta viga está sujeita a um momento flector e a um momento torsor, que surgem devido à geração de tração pela própria pá. Depois de uma análise aerodinâmica da pá, o utilizador pode definir um material para a mesma, bem como selecionar um conceito de construção entre os disponíveis e escolher o ponto para o qual quer analizar a deformação a que a pá está sujeita. Os resultados são apresentados na forma de gráficos de deslocamento e incremento ao ângulo de torção ao longo da envergadura da pá. Este módulo estrutural permite que o utilizador leve a cabo uma iteração adicional durante o projecto, e que garante que a pá não deformará excessivamente quando estiver em operação. O módulo estrutural permite ainda estimar o peso e o volume de cada pá, algo importante para o caso concreto do dirigível MAAT, uma vez que terá um grande número de hélices. O JBLADE é um software, desenvolvido como um código open source, escrito em linguagem C++/QML e compilado utilizando Qt Creator. O software mantém todas as funcionalidades originais do módulo XFOIL originalmente desenvolvidas no XFLR5, que permitem o projecto e a optimização de perfis para um dado ponto de projecto. O JBLADE possui uma interface gráfica e através da qual é possível executar todos os passos necessários ao projeto e análise de desempenho de uma hélice. O software permite que a pá seja introduza como um número arbitrário de secções, caracterizadas pela sua posição radial, corda, ângulo de incidência, comprimento, perfil e ainda pela polar 360º associada ao perfil. Este software permite também uma visualização e manipulação gráfica em 3 dimensões da pá/hélice, ajudando o utilizador a detetar possíveis inconsistências. O JBLADE também permite uma visualização direta e gráfica dos resultados das simulações de desempenho da hélice, tornado o código acessível e intuitivo. Uma vez que todos os módulos internos do JBLADE estão interligados, são evitadas operações demoradas de importação e exportação de dados, diminuindo assim possíveis erros criados pelo utilizador durante este processo. O código foi desenvolvido como um código aberto, para a simulação de hélices, e que tem a capacidade de estimar o desempenho de uma determinada geometria nas condições de operação do seu ponto de projeto e fora desse ponto de projeto. Como explicado anteriormente, uma vez que este trabalho foi desevolvido no âmbito do projecto MAAT, o desenvolvimento do software foi focado no projeto de hélices para dirigíveis xiv

15 de grande altitude. Para validar as modificações e os modelos desenvolvidos neste software foram utilizadas diferentes geometrias, provando que o JBLADE pode ser utilizado para projetar e otimizar hélices para diferentes finalidades. O procedimento de simulação de uma hélice foi validado, garantindo que pode ser utilizado um ponto intermédio e a distribuição correspondente dos números de Reynolds e de Mach. Foi ainda validado o número de pontos necessário para definir um perfil no sub-módulo XFOIL, mostrando que acima de 200 pontos não existem diferenças significativas no cálculo do desempenho do perfil, para um dado número de Reynolds. O novo método anteriormente apresentado para estimativa da previsão do coeficiente de arrasto foi também validado, e o seu efeito na previsão do desempenho das hélices foi demonstrado. O JBLADE foi ainda extensivamente validado através da comparação com dados experimentais apresentados na literatura, nomeadamente e com outros códigos numéricos disponíveis. Para garantir que o XFOIL poderia ser utilizado como ferramenta de previsão do desempenho de um perfil para um dado ponto de operação, foram feitas simulações para os perfis E387 e S1223 e comparadas com dados obtidos através de simulações de dinâmica dos fluidos computacional. Nestas simulações foram utilizados o modelo de turbulência k-ω Shear Stress Transport (SST) e uma versão remodelada do modelo de transição k-kl-ω. O modelo de transição k-kl-ω foi utilizado uma vez que prever o ponto de transição ao longo da corda é essencial para conseguir calcular correctamente o desempenho dos perfis que operam a baixos números de Reynolds (60 000<Re< ). Os resultados mostraram que o XFOIL consegue prever o desempenho dos perfis tão bem quanto os modelos de turbulência e de transição utilizados nas simulações de dinâmica dos fluidos computacional. Além disso, o XFOIL tem ainda a vantagem de as simulações serem mais rápidas e de necessitar de muito menos recursos computacionais quando comparado com as simulações de dinâmica dos fluidos computacional. O XFOIL pode, assim, continuar a ser utilizado como ferramenta de cálculo para o desempenho dos perfis que serão utilizados ao longo das pás da hélice. Durante este trabalho foi ainda desenvolvida uma nova instalação experimental, que foi posteriormente utilizada na validação do JBLADE. Esta instalação experimental, aplicada no túnel de vento do Departamento de Ciências Aeroespaciais da Universidade da Beira Interior foi validada através da comparação das medições obtidas para uma hélice com dados experimentais obtidos para essa mesma hélice noutras instalações experimentais. Além da validação da instalação experimental, foi construída e testada uma réplica da hélice APC 10 x7 SF, fornecendo dados adicionais para a validação do JBLADE. É apresentado todo o processo de desenho da réplica da hélice APC 10 x7 SF no software CAD bem como os passos necessários para a construção dos moldes. Foram desenhados 2 moldes fémea no software CATIA e posteriormente maquinados utilizando uma fresadora controlada por computador. Para obter a hélice final foi colocada fibra de carbono no interior dos moldes, sendo estes posteriormente fechados. Foi então introduzida resina epoxy, de modo a preencher todas as xv

16 cavidades e obter uma hélice tão próxima quanto possível da hélice original. Os resultados experimentais foram depois comparaddos com as simulações efectuadas no JBLADE, mostrarando uma boa concordância entre as estimativas do JBLADE e as medições experimentais. Através de tudo o que foi anteriormente apresentado foi possivel concluir que que o JBLADE pode ser utilizado para projetar e estimar o desempenho de hélices, que entre outras aplicações, poderão ser utilizadas pelo dirigível cruzador do projecto MAAT. xvi

17 Table of Contents Agradecimentos... vii Support... vii Resumo... ix Palavras-chave... x Abstract... xi Keywords... xii Resumo Alargado... xiii Table of Contents... xvii List of Figures... xxi List of Tables... xxvii Nomenclature... xxix Latin Terms... xxix Greek Symbols... xxxii Acronyms... xxxiii Chapter Motivation Objectives Contributions Thesis Outline... 3 Chapter Historical Developments of Propeller Theory Present Status of Propeller Aerodynamics Available Propeller Design Codes Propeller Theory Momentum Theory Blade Element Theory Blade Element Momentum Theory Prandtl Tip and Hub Losses Corrections Post Stall Models Propeller Momentum Theory with Slipstream Rotation Propeller Inverse Design Methodology Forces acting on a Propeller Volume and Blade Mass Estimation Blade Bending Estimation Blade Twist Deformation Present Research Contributions to Propeller Aerodynamics Modelling New 3D Flow Equilibrium Model New Methods for CD90 Prediction Airfoil Leading Edge Radius Method xvii

18 Airfoil yc at xc = Method Chapter Software Overview Airfoil design and analysis º AoA Polar extrapolation Blade definition Propeller inverse design Parametric simulation Propeller definition and simulation Number of blade elements Foil interpolation Fluid density and viscosity Convergence criteria Relaxation factor Reynolds Number Correction Structural sub-module Creating and editing materials JBLADE Software Validation Propeller Geometries NACA Technical Report NACA Technical Report Adkins and Liebeck Propeller APC 11 x Simulation Procedure Validation Methods for Drag Coefficient at 90º Prediction Validation NACA Technical Report NACA Technical Report Post-Stall Models NACA Technical Report Inverse Design Methodology Validation Adkins and Liebeck Propeller JBLADE vs Other BEM Codes NACA Technical Report NACA Technical Report Adkins and Liebeck Propeller APC 11 x4.7 Propeller Structural Sub-Module Validation CATIA simulation validation Blade s geometrical properties validation JBLADE bending validation JBLADE twist deformation validation xviii

19 Chapter Theoretical Formulation k-kl-ω model Shear Stress Transport k-ω model Low Reynolds Correction XFOIL Numerical Procedure Mesh Generation Boundary Conditions Results E387 Airfoil S1223 Airfoil Chapter High Altitude Propellers Egrett Condor Pathfinder Perseus Strato 2C Theseus MAAT Cruiser Requirements Propeller Design and Optimization Airfoil Development A New High Altitude Propeller Geometry Design Concept Chapter APC 10 x7 SF Propeller CFD procedure D Flow equilibrium validation Performance prediction MAAT Cruiser Propeller CFD procedure Performance prediction Chapter Experimental Setup Wind tunnel Thrust Balance Concept Thrust and Torque Measurements Propeller rotation speed measurement Free stream flow speed measurement Balance Calibration Test Methodology xix

20 7.2 - Wind Tunnel Corrections Boundary corrections for propellers Motor fixture drag correction Validation of the Test Rig Sampling time independence Measurements repeatability Propeller performance data comparison APC 10 x4.7 Slow Flyer APC 11 x5.5 Thin Electric Uncertainty Analysis APC 10 x7 SF Propeller Inverse Design Propeller CAD inverse design Moulds manufacture Propeller manufacture Results and Discussion Chapter Summary and conclusions Future Works Bibliography Appendix A A.1 Freestream Velocity A.2 Advance Ratio A.3 Thrust Coefficient A.4 Power Coefficient A.5 Propeller Efficiency Appendix B List of Publications Peer Reviewed Journal Papers Peer Reviewed International Conferences Peer Reviewed National Conferences B.I Validation of New Formulations for Propeller Analysis B.II Propeller Performance Measurements at Low Reynolds Numbers B.III A Comparison of Post-Stall Models Extended for Propeller Performance Prediction 191 B.IV High altitude propeller design and analysis B.V XFOIL vs CFD performance predictions for high lift low Reynolds number airfoils xx

21 List of Figures Figure Propeller Stream-tube (Rwigema, 2010) Figure 2.2 Geometry of rotor annulus (Prouty, 2003) Figure Blade element geometry and velocities at an arbitrary radius position (Drela, 2006) Figure Flowchart of inverse design procedure in JBLADE Figure 2.5 (a) Illustration of propeller torque bending force and propeller centrifugal force. Reproduced from Mechanics Powerplant Handbook (1976) (b) Illustration of propeller trust bending force Figure 2.6 Scheme of a cantilevered beam with a group of arbitrary positioned loads Figure 2.7 Illustration of a beam subjected to a twisting moment Figure Measured airfoil drag coefficient at 90 degrees AoA vs airfoil leading edge radius. The airfoil data correspond to those of Table Figure Comparison between original correlation, described by Timmer (2010) and improved correlation. The airfoil data correspond to those of Table Figure JBLADE software structure representing the internal sub-modules interaction.. 32 Figure XFOIL sub-module in JBLADE Figure Polar Extrapolation Sub-Module Screen Figure Blade Definition Sub-Module Figure Blade definition/inverse design sub-module in JBLADE Figure 3.6 Parametric Simulation Sub-Module in JBLADE Figure 3.7 Simulation sub-module overview Figure Flowchart of simulation procedure in JBLADE Figure Simulation definition dialog box Figure 3.10 Representation of the sections and the sinusoidal spaced elements along the blade Figure 3.11 Structural sub-module overview Figure 3.12 New material definition dialog box Figure NACA Technical Report No. 594 (Theodorsen et al., 1937) propeller (a) propeller geometry (b) propeller visualization in JBLADE Figure NACA Technical Report No. 530 (Gray, 1941) 6267A-18 propeller (a) propeller geometry (b) propeller visualization in JBLADE Figure Propeller geometry presented by Adkins & Liebeck (1994) (a) propeller geometry (b) propeller visualization in JBLADE Figure APC 11 x4.7 propeller(brandt et al., 2014) (a) propeller geometry (b) Illustration of the propeller inside JBLADE Figure 3.17 E387 airfoil polars. (a) Validation of polar calculation using different number of points to define the airfoil in XFOIL (b) Comparison between XFOIL and experimental studies (Selig & Guglielmo, 1997) different Reynolds numbers xxi

22 Figure Possible reference lines for blade pitch angle measurements Figure Validation of calculations for the Propeller C of NACA TR 594 (Theodorsen et al., 1937) using a distribution of averaged Reynolds and Mach Numbers along the blade: (a) thrust coefficient (b) power coefficient, (c) propeller efficiency Figure Modelation influence on the simulated propeller performance: (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure 3.21 Influence of the 360 polars extrapolation in the propeller performance and comparison with data from NACA TR 594 for θ 75 =45 : (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Influence of the 360 polars extrapolation in the propeller performance and comparison with data from NACA TR 530 for θ 75 =30 : (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Influence of the 360 polars extrapolation in the propeller performance and comparison with data from NACA TR 530 for θ 75 =40 (a) thrust coefficient (b) power coefficient, (c) propeller efficiency Figure Influence of the 360 polars extrapolation in the propeller performance and comparison with data from NACA TR 530 for θ 75 =50 (a) thrust coefficient (b) power coefficient, (c) propeller efficiency Figure Comparison between data predicted by JBLADE using different post-stall models and data from NACA TR No. 594 (Theodorsen et al., 1937) for θ 75 =30 (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Comparison between data predicted by JBLADE using different post-stall models and data from NACA TR No. 594 (Theodorsen et al., 1937) for θ 75 =45 (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Validation of the inverse design methodology. (a) blade incidence angle (b) chord Figure Results of NACA TR 594 (Theodorsen et al., 1937) for θ 75 =15 (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Results of NACA TR 594 (Theodorsen et al., 1937) for θ 75 =30 (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure 3.30 Results of NACA TR 594 (Theodorsen et al., 1937) for θ 75 =45 (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure 3.31 Results of NACA TR 530 (Gray, 1941) for θ 75 =30 (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Results of NACA TR 530 (Gray, 1941) for θ 75 =40 (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Results of NACA TR 530 (Gray, 1941) for θ 75 =50 (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Comparison between data predicted by JBLADE and data obtained from Adkins & Liebeck (1994). (a) thrust coefficient (b) power coefficient (c) propeller efficiency xxii

23 Figure Comparison between JBLADE predictions and data obtained from UIUC database for an APC 11 x4.7 for 3000 RPM (Brandt et al., 2014). (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Comparison between JBLADE predictions and data obtained from UIUC database for an APC 11 x4.7 for 6000 RPM (Brandt et al., 2014). (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Airfoil performance of the APC 11 x4.7 propeller obtained at r/r=0.75 for 3000 RPM and 6000 RPM Figure 3.38 Example of a bending Simulation in CATIA v Figure 3.39 Mesh independency study performed in CATIA for Blade Figure 3.40 Comparison of Bending calculated in JBLADE and CATIA for Blade Figure 3.41 Comparison of Bending calculated in JBLADE and CATIA for Blade Figure 3.42 Comparison of Bending calculated in JBLADE and CATIA for Blade Figure 3.43 Illustration of the skin deformation calculated in CATIA Figure 3.44 Comparison of Bending calculated in JBLADE and CATIA for Blade Figure 3.45 Comparison of Bending calculated in JBLADE and CATIA for Blade Figure 3.46 Example of a Twist Deformation Simulation in CATIA V Figure 3.47 Trailing Edge Displacement Comparison for Blade Figure 3.48 Trailing Edge Displacement Comparison for Blade Figure 3.49 Leading Edge Displacement Comparison for Blade Figure 3.50 Trailing Edge Displacement Comparison for Blade Figure 3.51 Trailing Edge Displacement Comparison for Blade Figure Detail of the mesh around the airfoil used to obtain k-ω and k-kl-ω predictions. 89 Figure Aerodynamic characteristics of the E 387 airfoil measured at Penn State UIUC wind tunnel (Sommers & Maughmer, 2003) compared with the numerical simulations results Figure Comparison of E387 airfoil pressure distributions measurements (McGee et al., 1988) and results obtained with the CFD models and XFOIL, for Re = 2.0x10 5. (a) α=0º (b) α=4º Figure (a) Transition position of the E387 airfoil upper and lower surfaces. (b) Drag polar of E387 for Re= 2.0x Figure 4.5 Comparison between UIUC measurements (Selig & Guglielmo, 1997) and results obtained by CFD models and XFOIL for S1223 airfoil for Re = 2.0x10 5. (a) C L vs C D (b) C L vs α Figure Comparison of S1223 airfoil pressure distributions for Re = 2.0x10 5. (a) α=4º (b) α=8º Figure 5.1 Parametric study of the thrust for each propeller and their respective diameter Figure Airfoils comparison performed in JBLADE s XFOIL sub-module for Re=5.00x10 5 and 3/2 M=0.1 (a) C L vs C D (b) C L /C D vs C L xxiii

24 Figure 5.3 -Base and final airfoils shapes comparison and their pressure coefficient distribution for Re=5.70x10 5 and α=6.0º Figure Comparison between NACA 63A514 and improved airfoil for Re= 5.70x10 5. (a) C L vs α (b) C L vs C D (c) L/D vs C L (d) L 3/2 /D vs C L Figure (a) Comparison of propellers geometries (b) L 3/2 /D Propeller (c) L/D Propeller. 101 Figure Final Reynolds and Mach numbers distribution along blade radius for V = 28m/s at r/r= Figure APC 10 x7 SF propeller geometry (Brandt et al., 2014) and its shape after introduced in JBLADE Figure 6.2 Domain dimensions used to simulate the APC 10 x7 SF propeller Figure 6.3 Domain and boundary conditions used to simulate the APC 10 x7 SF propeller. 105 Figure 6.4- Distribution of the cells on the blade surface Figure 6.5 CFD Simulations mesh independency tests performed for APC 10 x7 SF propeller for 3000 RPM and 5 m/s. (a) thrust coefficient (b) power coefficient, (c) propeller efficiency Figure Tangential velocity distribution along an APC 10x7 SF propeller (Brandt et al., 2014) blade radius, at 1 m behind the propeller plane, for CFD, original BEM formulation and new proposed 3D Flow Equilibrium model Figure 6.7 Performance prediction comparison for APC 10 x7 SF propeller (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure Pressure distribution on blade surface and velocity magnitude distribution on the iso-surfaces for V =1 m/s and 3000 RPM Figure Example of the blade geometry transformed into a CAD part for meshing purposes Figure Representation of the computational domain and its boundary conditions Figure Distribution of the cells on the blade surface Figure Mesh independency study made for L 3/2 /D propeller at V=30 m/s. (a) thrust coefficient (b) power coefficient, (c) propeller efficiency Figure Comparison between data predicted by JBLADE and CFD for the designed propellers: (a) thrust coefficient (b) power coefficient, (c) propeller efficiency Figure Skin friction coefficient distribution on upper surface for an advance ratio of (a) L 3/2 /D Propeller (b) L/D Propeller Figure Skin friction coefficient distribution on lower surface for an advance ratio of (a) L 3/2 /D Propeller (b) L/D Propeller Figure Pressure distribution on upper surface for an advance ratio of 0.91 (a) L 3/2 /D Propeller (b) L/D Propeller Figure Pressure distribution on upper surface for an advance ratio of (a) L 3/2 /D Propeller (b) L/D Propeller Figure 7.1 Wind tunnel of Aerospace Sciences Department Figure 7.2 Thrust Balance Concept (Alves, 2014) xxiv

25 Figure 7.3 Sensors specifications (a) Thrust load cell (b) Torque Reaction Sensor (c) Shielded Connector Block Figure Photoreflector circuit s schematics (Santos, 2012) Figure 7.5 Wind tunnel Schematics with representation of the static pressure ports location Figure 7.6 Illustration of calibrations procedure (Alves, 2014). (a) Torque sensor (b) Thrust load cell Figure 7.7 Flowchart of the test methodology Figure Torque and Thrust outputs during the convergence and data collection phases. 124 Figure Effect of the propeller in a closed test section Figure 7.10 Number of samples independence test. (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure 7.11 Three days testing. (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure 7.12 APC 10 x4.7 Slow Flyer Propeller Figure 7.13 APC 10 x4.7 Slow Flyer performance comparison for 4000 RPM. (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure 7.14 APC 10x4.7 Slow Flyer performance comparison for 5000 RPM. (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure 7.15 APC Thin Electric Propeller Figure APC 11 x5.5 Thin Electric performance comparison for 3000 RPM. (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure APC 11 x5.5 Thin Electric performance comparison for 4000 RPM. (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure APC 11 x5.5 Thin Electric performance comparison for 5000 RPM. (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure 7.19 Propeller CAD design steps (a) airfoils import and leading edge alignment (b) airfoils translation to their quarter chord point (c) airfoils pitch setting Figure Top view of final blade geometry Figure 7.21 View of the blade within the mould, showing the mould halves matching Figure 7.22 (a) Illustration of the mould after the roughing path. (b) )Illustration of the mould after the finishing path Figure 7.23 Final obtained mould Figure 7.24 Carbon fibre placement inside the moulds Figure 7.25 Closed moulds with carbon fibre inside and with a hole to allow the moulds fill with epoxy resin Figure 7.26 Final manufactured propeller, representing the APC 10 x7 SF propeller in JBLADE Software Figure APC 10 x7 Slow Flyer static performance comparison with JBLADE predictions. (a) propeller thrust (b) propeller torque xxv

26 Figure APC 10 x7 Slow Flyer performance comparison with JBLADE Predictions for 3000 RPM (a) thrust coefficient (b) power coefficient (c) propeller efficiency Figure APC 10 x7 Slow Flyer performance comparison with propeller built for a rotational speed of 6000 RPM (a) thrust coefficient (b) power coefficient (c) propeller efficiency xxvi

27 List of Tables Table Leading edge radius calculations and errors due to the least square method approximation Table 2.2 Drag coefficient at 90 degrees measured and calculated by the two developed methods for a set of airfoils Table 3.1 Input data for propeller inverse design Table 3.2 Blade Definition for Structural Sub-Module validation Table 3.3 Properties of the Materials used in the blades Table 3.4 Volume and Mass comparison using JBLADE and CATIA V Table 3.5 2D Airfoil properties comparison using JBLADE and CATIA Table 3.6 2D properties comparison using JBLADE and CATIA for intermediate sections of Blade Table 5.1- High-altitude propeller data Table 5.2- Initial Considerations for the study of number of propellers Table 5.3- MAAT cruiser propulsive system properties Table 5.4- Atmosphere Conditions for an altitude of 16 km Table 6.1- Number of cells of different meshes used in the mesh independency tests Table 6.2- Number of cells of different meshes used in the mesh independency tests Table 7.1- Convergence criteria to achieve wind tunnel steady state Table 7.2- Convergence criteria to achieve wind tunnel steady state Table 7.3- Convergence criteria to achieve wind tunnel steady state Table 7.4- APC 10 x7 Slow Flyer propeller uncertainty for 4000 RPM xxvii

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29 Nomenclature Latin Terms A = Area of the actuator disk, m 2 A 0 = k kl ω model freestream vortex surface area A 1 = Cross-section area of the settling chamber, m 2 A 2 = Cross-section area of the test section, m 2 a a a a old A core = Axial induction factor = Axial induction factor of the previous iteration = Area of core airfoil A ext = Area of exterior airfoil, m 2 A int = Area of interior airfoil, m 2 a t a told B b c C a C D c d 2D c d 3D = Tangential induction factor = Tangential induction factor of the previous iteration = Number of blades = Length of the beam, m = Blade local chord, m = Axial force coefficient = Airfoil drag coefficient = Two dimensional drag coefficient = Three Dimensional drag coefficient C D90 = Airfoil drag coefficient at 90º C DRef C INT C L C lmax c lpot c lnon_rot c r c lrot c l 3D c l 2D c p C t c t C ω C ω1 = Reference airfoil drag coefficient = k kl ω model intermittency damping constant = Airfoil lift coefficient = Maximum lift coefficient of the airfoil = Potential flow lift coeficient = airfoil lift coefficient of non-rotating airfoil = Blade local chord, m = Airfoil lift coefficient of rotating airfoil = Three Dimensional lift coefficient = Two dimensional lift coefficient = power coefficient = Tangential force coefficient = Thrust coefficient = Turbulent kinetic energy dissipation = Specific turbulent kinetic energy dissipation xxix

30 C ω2 C ω3 C ω R C λ,y C μ C SS D D D L D p D T D ω E F F a f INT new f INT F t f ν f W f ω f SS F 1, F 2 G = Rate of the turbulent kinetic energy dissipation = Scale of the turbulent kinetic energy dissipation rate = Constant to control the turbulent kinetic energy dissipation rate = Calibration constant to control the influence of the distance to the wall = k kl ω model turbulent viscosity coefficient = Shear-Sheltering constant = Drag, N = Component of drag force on the original system of coordinates = k kl ω model laminar fluctuations kinetic energy destruction term = Propeller diameter, m = k kl ω model turbulent kinetic energy destruction term = Cross diffusion term = Young Modulus, GPa = Prandtl s correction factor = Axial blade force, N = k kl ω model intermittency damping function = k kl ω model new intermittency damping function = Tangential blade force, N = k kl ω model viscous damping function = k kl ω model viscous wall damping function = k kl ω model kinematic wall effect damping function = k kl ω model shear-sheltering damping function = Blending functions = Circulation function g = Gravity acceleration, m/s 2 g cl G ω G k = Lift coefficient correction function = Generation of ω = Turbulence kinetic energy generation due to mean velocity gradients I xx = Moment of inertia, m 4 I yy = Moment of inertia, m 4 J k kl k L k T,s k TOT L L LE Radius = Advance Ratio = Turbulent kinetic energy = k kl ω model laminar fluctuations kinetic energy = k kl ω model laminar kinetic energy = k kl ω model effective small-scale turbulent kinetic energy = k kl ω model total fluctuatin = lift force, N = Component of lift force on the original system of coordinates = Airfoil leading edge radius calculated with least square method xxx

31 M = Bending moment, N.m m = Mass flow rate, kg/s M Blade m e m 0 N n P p 1 p 2 P i = Blade s Mass, kg = Mass flow rate at the exit, kg/s = Mass flow rate at the unperturbed flow, kg/s = Amplification factor = Rotation speed, rps = Power, W = Pressure at settling chamber = Pressure at test section = Arbitrary load applied to a beam, N P c = Power coefficient, 2P/ρV 3 πr 2 P c = Power coefficient derived with respect to the non-dimensional radius P k P kl P kt,s Q R r R BP R hub R LE R NAT Re exp Re T Re T new Re r Re Ref S S k, S ω T t = k kl ω model turbulent production term = k kl ω model laminar fluctuations kinetic energy production term = k kl ω model turbulent kinetic energy production term = Torque, N.m = Propeller tip radius, m = radius of blade element position, m = k kl ω model bypass transition energy transfer function = Propeller hub radius, m = airfoil leading edge radius = k kl ω model natural transition energy transfer function = Exponential value for Reynolds number correction = Turbulence Reynolds number = New turbulence Reynolds number = Local Reynolds number = Reference Reynolds number = Mean flow shear = Dissipation of k and ω = Thrust, N = airfoil thickness T/A = Disk Loading, N/m 2 T c = Thrust coefficient, 2T/ρV 2 πr 2 T c = Thrust coefficient, derived with respect to non dimensional radius Tu = Absolute turbulent intensity V Blade = Blade Volume, m 3 V BladeCore = Volume of the core of the blade, m 3 V Bladeskin = Volume of the skin of the blade, m 3 xxxi

32 V e V p = Induced Velocity at the far wake, m/s = Velocity at propeller s disk, m/s V skin = Volume of the skin of the blade, m 3 V t75 = Tangential velocity at 75% of the blade radius, m/s V x V xw V 0 V 1 V 2 W W a W a W r W t x x/c X centroid Y centroid y + = Axial or tangential flow velocity components at the disk = Axial or tangential flow velocity components at the wake = Velocity of the unperturbed flow, m/s = Velocity at the settling chamber, m/s = Velocity at the test section, m/s = element relative velocity, m/s = element axial velocity, m/s = Average axial velocity, m/s = Local freestream speed, m/s = Element tangential velocity, m/s = Non-dimensional distance, Ωr/W = non dimensional x position = Horizontal coordinate of the airfoil centroid, mm = Vertical coordinate of the airfoil centroid, mm = Non-dimensional wall distance (y/c) (x/c)= = non dimensional y position at x/c = Y k, Y ω = Dissipation of k and ω z 1 z 2 = Height of settling chamber center line = Height of test section center line Greek Symbols α α α cl max α cl 0 α T Δr Δc l Δc d δ Γ Γ k, Γ ω ε ε conv ζ = angle of attack, deg = Damping turbulent viscosity coefficient = Angle of attack of maximum lift coefficient, deg = Angle of attack of zero lift coefficient, deg = k kl ω model effective turbulent diffusivity = Width of the annulus, m = Difference between lift coefficient with and without separation = Difference between drag coefficient with and without separation = Bending displacement, m = Circulation = Effective diffusivity of k and ω = Drag-to-lift ratio, D/L = User-defined convergence criterion = Displacement velocity ratio, v /V xxxii

33 η θ θ 75 θ Axis θ LowerSurface λ λ eff λ T = Propeller efficiency = incidence angle, deg = Propeller twist angle at 75 % of the blade span = incidence angle coincident with airfoil axis = incidence angle coincident with airfoil lower surface = Speed ratio, W/ΩR = k kl ω model effective turbulent length scale = k kl ω model turbulent length scale μ = Dynamic viscosity,n.s/m 2 μ t ν T,s ν T,l ξ = Turbulent viscosity = k kl ω model small scale turbulent kinematic viscosity = k kl ω model large scale turbulent kinematic viscosity = Non-dimensional radius, r/r = λx ρ = air density, kg/m 3 ρ mat = Material density, kg/m 3 σ k, σ ω σ r φ φ t Ω Ω v ω ω relax Acronyms = Turbulent Prandtl numbers for k and ω = rotor solidity ratio = inflow angle, deg = Tip inflow angle AoA = Angle of Attack = rotation speed, RPM = Mean flow vorticity = Specific dissipation rate = User-defined relaxation factor APC = Advanced Precision Composites Commercial brand of propellers BEM = Blade Element Momentum CFD = Computational Fluid Dynamics FEM = Finite Element Method FVM = Finite Volume Method MAAT = Multibody Advanced Airship for Transportation MRF = Multiple Reference Frames NACA = National Advisory Committee for Aeronautics RANS = Reynolds-Averaged Navier Stokes SF = Slow Flyer TR = Technical Report UBI = University of Beira Interior VTOL = Vertical Take Off and Landing XFLR5 = Software Developed by Deperrois, A. xxxiii

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37 Chapter 1 Introduction Motivation The problems caused by growth in the transportation sector, e.g. the rise of fuel consumption and cost, as well as pollution and consequent climate change led to a reconsideration of the transportation systems by the most economically advanced nations (Wilson, 2004). Nowadays, despite all technologic developments, as we proceed in the 21 st century, we may be about to witness the return of slower air transport as a means of increasing energy efficiency and business profitability. Slowing down aircrafts can take us towards the airship. After the initial developments until the 1930s, and during some decades, the airships were only considered as a mere curiosity. At their peak, in the late 1930s, airships were unrivaled in transoceanic transportation. Nowadays, they can be used effectively as platforms for different purposes (van Eaton, 1991; Liao & Pasternak, 2009; Morgado et al., 2012; Wang et al., 2009) especially activities that require long endurance or hovering for long time. In Europe, the development of new airships is being supported by European Union through the Multibody Concept for Advanced Airship for Transport (MAAT (Dumas et al., 2011)) project. The MAAT Project was funded by European Union through the 7th Framework Programme and it aims to investigate the possibilities to develop a new stratospheric airship as a global transportation system. This collaborative project aims to develop a heavy lift cruiser-feeder airship system in order to provide middle and long range transport for passengers and goods. The MAAT system is composed by the cruiser and the feeder modules. The feeder is a Vertical Take Off and Landing (VTOL) Vehicle which ensures the connection between the ground and the cruiser. It can go up and down by the control of buoyancy force and displace horizontally to join to the cruiser. The cruiser is conceived to move mostly in a horizontal way at high 1

38 altitude. Since the MAAT project has the objective of operating airships at stratospheric altitudes, propellers are a valid option to the airships propulsion. The presented work was integrated in the Multibody Advanced Airship for Transport (MAAT) project. A distributed propulsion concept for the MAAT cruiser airship based on very low tip speed propellers can bring advantages in terms of minimizing the needed propulsion power for this solar powered airship. The problem is the very low average Reynolds number of the propellers blade, resulting from the extremely low air density at the cruising altitude of 16 km. The existing design tools suited for the development of such low Reynolds propellers show limitations that cannot be overran Objectives The objective of the thesis is to develop a software tool capable to design and optimize propellers for the MAAT project airship application. A detailed literature review and state of the art research is to be carried out. Appropriate analysis and optimization computational tools must be developed and/or integrated. Furthermore, a complete validation of the tool should be performed, through the comparison with numerical and experimental data available in the literature. In order to achieve these goals the following topics must be addressed: Development of a software capable to design and optimize propellers suitable to highaltitude/low Reynolds usage; Integration of an inverse design methodology in order to design new propellers for distinct applications; Estimation of the blade tip displacement and torsional angle change due to the thrust, blade sweep and pitching moment at a given operating condition; Validation of the software through different comparisons with both numerical and experimental data; Design and analysis of a propeller to use in the MAAT cruiser airship Contributions The main contributions of this dissertation lie on the characteristics of the new software tool suitable for the design and optimization of new propellers. Although the computational tool partly uses well established methods for both airfoil and propeller aerodynamic analysis, it also embeds new models that improve its accuracy and applicability to the particular low Reynolds numbers propeller design making it very useful and powerful. A new model for the 3D flow equilibrium (see Section 2.4.1) was developed to account with the real 3D flow passing the propeller disk. In addition, a new method to predict the airfoil drag 2

39 coefficient at an angle of attack of 90º C D90 based on the airfoil leading edge (see Section 2.4.2) was developed and it proved to be more accurate than the methods previously used in other BEM s based Software. An inverse design capability was integrated in the software, allowing a faster propeller design from the known propeller operating point as presented in Section In addition, a Structural sub-module (see Section 3.2.7) was also integrated in the software, providing the capability of propeller weight estimation depending on the material and the structural concept used in the propeller. This sub-module also allows the determination of tip displacement at different propeller operating conditions. Furthermore, this sub-module also allows the computation of the twist angle change due to the propeller operating conditions, allowing an additional layer of iteration during the propeller design. Since the software is an in-house development code, further enhancements can be easily implemented in order to account for the complete propulsion system. The long term goal of the JBLADE Software development is to provide a user-friendly, accurate, and validated opensource code that can be used to design and optimize propellers for distinct applications Thesis Outline After this introductory chapter, in which the motivation, objectives and contributions of this thesis were described, the present work is divided in the sections described below. Chapter 2 presents the historical development of propeller theory. Furthermore, this chapter presents a state of the art of the low Reynolds number propeller design. In addition, this chapter also includes the detailed description of the formulations theories used inside the JBLADE Software. Chapter 2 includes the contributions to the state of the art of propeller theory developed during this thesis. Two different main contributions are presented and discussed in detail: the 3D flow equilibrium and the new method to predict the airfoil drag coefficient based on the airfoil s leading edge radius. Chapter 3 presents the JBLADE Software architecture in detail. The chapter begins with the overview of the XFOIL and BEM Modules interaction. Furthermore, each sub-module and their capabilities are described and discussed in detail. In addition, Chapter 3 also presents the different JBLADE validations. The data from NACA TR 594 was used to validate the simulation procedure as well as the JBLADE performance prediction. NACA TR 530 Report data were used to validate the new methods for the airfoil C D90 prediction. This chapter also presents the validation of the inverse design sub-module through the comparison with the original Adkins and Liebeck implementation. Furthermore, the validation of the structural sub-module is presented by comparing the bending and torsional predictions of some operation loaded blades with Finite Element Method (FEM) simulations in CATIA V5. 3

40 Chapter 4 presents a comparison between XFOIL and conventional turbulence and transition models. The chapter describes the theoretical formulation of each model as well as the numerical procedure used along the simulations. Two different airfoils were used to verify the accuracy of XFOIL against conventional Computational Fluid Dynamics (CFD). Chapter 5 presents the development and optimization of a new propeller suitable for the MAAT cruiser airship. In this chapter the development of the airfoil used in the propeller is also described. Two different propellers were developed, following different methodologies and their geometries are shown is Chapter 5. Chapter 6 presents the Computational Fluid Dynamics simulations of different propellers. It shows the numerical procedure used to simulate the APC 10 x7 SF propeller and the propellers developed in Chapter 5. The APC 10 x7 SF was also used to validate the new 3D flow equilibrium, presented in Chapter 2. Furthermore, the performance prediction of JBLADE is also compared with CFD predictions and experimental data from UIUC propeller data site. The propellers developed for the MAAT cruiser airship were simulated and their performance was compared with the JBLADE predictions. Chapter 7 presents the experimental work developed in the University of Beira Interior s subsonic wind tunnel. The development and validation of the experimental procedure is shown, followed by the uncertainty analysis of the data obtained from the experiments. In addition, the process of replication of the APC 10 x7 SF propeller is described in detail. To finalize, the original APC 10 x7 SF propeller is tested and compared with the performance of its replica. Chapter 8 presents the general discussion and conclusions of the work developed during the present dissertation. At the end of the chapter future works are proposed for the continuous development of the JBLADE Software as well as possible improvements in the test rig, in order to keep developing more accurate tools and more efficient propellers. 4

41 Chapter 2 Propeller Design Theory Historical Developments of Propeller Theory Propellers are being used to generate thrust from the beginning of powered flight (Colozza, 1998; Dreier, 2007). The first developments related to the theory of propellers occurred in the 19th century with Rankine & Froude (1889) and Froude (1920) through a work mainly focused on marine propellers. They established the essential momentum relations governing a propulsive device in a fluid medium. Later, Drzewiecki (1892) presented a theory of propeller action where blade elements were treated as individual lifting surfaces moving through the medium on a helical path. However, he did not take into account the effect of the own propeller induced velocity at each element. In 1919, Betz & Prandtl (1919) stated that the load distribution for lightly loaded propellers with minimum energy loss is such that the shed vorticity forms regular helicoidal vortex sheets moving backward undeformed behind the propeller. Thus, the induced losses of propellers will be minimized if the propeller slipstream has a constant axial velocity and if each cross section of the slipstream rotates around the propeller axis like a rigid disk (Eppler & Hepperle, 1984). Prandtl, as described in Glauert (1935) found an approximation to the flow around helicoidal vortex sheets which is good if the advance ratio is small and improves as the number of blades increases. The approximation presented by Prandtl is still applied in simple mathematical codes. Goldstein (1929) found a solution for the potential field and the distribution of circulation for propellers with small advance ratios. This solution was still limited to lightly loaded propellers. Theodorsen (1948), through his study on the vortex system in the far field of the propeller, concluded that the Goldstein s solution for the field of a helicoidal vortex sheet remains valid, even for moderate/highly loaded propellers. In 1935 Welty & Davis (1935) described the steps needed to design and produce a new propeller according to the available material properties and introduce the light alloy propeller. Later, in 1936, Biermann (1936) developed one of the 5

42 first parametric studies, analysing the influence of some parameters during propeller design. He analysed the reduction in the design pitch angle as a function of the propeller operating speed and the thrust and/or power increase. In 1937, Caldwell (1937) studied the effect of the propeller s diameter and rotational speed on its efficiency for different operating conditions. McCoy (1939) presented a study in which he mentioned the improvement of the propeller s efficiency that can be expected if the engines are enclosed within the airplane or within the wing structure and driving shafts are used to drive the propellers. He concluded that the reduction in drag, the increase in lift, L/D ratio and in the propeller efficiency associated with extension shaft drives give for equal power a substantial improvement in entire aircraft s operation. Later, in 1944, he presented the functional requirements that have formed the basis for propeller development by the United States Army at that time (McCoy, 1944). In addition, he presented experimental results showing that reverse pitch propellers can be used to help the aircraft landing in shorter distances. In 1948, Ribner & Foster (1990) developed a computer code that allowed to determine the ideal efficiency of an ideal propeller. Approximately 10 years later, during 1955, Mccormick (1955) presented a Goldestein s propeller analysis, satisfying the Minimum Induced Losses (MIL) propeller wake condition but extended it to account for the hub radius influence. The MIL propeller wake condition is attributed to Betz in what he called the solid wake condition. The author shows that for a trailing vortex sheet of a given propeller pitch, when the hub s influence is included it increases the value of the bound circulation of the line vortex generating the sheet. In addition the author notices that the change varies inversely with the number of blades. During 1965, de Young (1965) derived the force and moment equations covering the propeller range of angle of attack from 0º to 90º. He made the expression independent of the blade shape, using a solidity based on an average blade chord. Additionally, he verified that his formulation shows an accuracy adequate to establish design criteria, to perform trend studies, to develop preliminary configuration and to estimate the propeller performance. During 1968, Hall (1969) developed a new method to analyse propeller blades at high angles of attack similar to the classical Prandtl s (Glauert, 1935) tip loss model. The developed tip loss factor is also a function of the number of the blades, nondimensional propeller radius and wake helix geometry. During 1974, Fanoe (1974) presented an expression for the aerodynamic pitch angle, valid for a propeller with an arbitrary number of blades in viscous flow to be used in the design of moderately loaded propellers. In 1978, Azuma & Kawachi (1979) derived a new momentum theory. This theory was based on the instantaneous momentum balance of the fluid with the blade elemental lift at each local station in the propeller disk. When they applied the theory to both steady and unsteady flow cases they achieved good results, with lower computational costs when compared with the vortex theory. In 1980, Larrabee (1979) analysed the steady air loads on the propeller and presented a practical design theory for minimum induced loss propellers. The method presented by Larrabee is a combination between 6

43 momentum theory, blade element theory and vortex theory. In 1986, Johnson (1986) presented a study in which the progress in development of advanced computational methods for rotarywing aerodynamics was examined. In the same year, Rizk & Jou (1986a, 1986b) developed a preliminary design code based on the finite volumes for solving the potential flow about a propeller by line relaxation. Although the code was able to calculate the transonic flow field around the propellers during the initial phase of the research, the authors decided to limit the investigation to subsonic flow calculations. They combined an analysis code with the singlecycle optimization approach to produce an efficient design code (Rizk, 1983, 1985). In 1989, Favier et al. (1989) investigated the isolated propeller aerodynamics both numerically and experimentally. They studied the propeller aerodynamic field over a large range of operating conditions of the axial flight regime. They concluded that their code predictions of both local and global aerodynamic coefficients were in good agreement with the experiments for the different propeller axial flight conditions. During 1988, Strash et al. (1998) presented a multi-grid Euler technique with a coupled blade element momentum module that can be used in the analysis of the propeller slipstream interference effects. Later on, Adkins & Liebeck (1994) presented improvements with small angle approximations and light load approximations, overcoming the restrictions in the method developed by Larrabee (1979). In 2002, Miley et al. (2002) analysed the design methods applied by the Wright brothers to their propeller. Additionally, the experimental investigation conducted by Miley showed that the Wright brothers developed a high efficiency low rotational speed propellers early in Present Status of Propeller Aerodynamics Although the literature of propeller aerodynamics is, in some aspects, dispersed and incomplete (Wald, 2006), the theories describing the propeller aerodynamics have been improved during the past decades. There are several methods available for the propeller design and analysis depending on the desired level of fidelity (Benini, 2004). The Computational Fluid Dynamics (CFD) is the most sophisticated method, consisting in three dimensional viscous flow models, including incompressible Reynolds-Averaged Navier Stokes (RANS) equations solved in an iterative way. However, as it is possible to observe in Chapter 4, if the airfoils are working at low Reynolds number environments the RANS CFD methods present some limitations in the prediction of the laminar flow region, leading to worst results when compared with other computational tools or even with experimental data. Between the most advanced methods is also the lifting surface methods. Some of the implementations can calculate near-wall effects since they contain the RANS equations to account for the viscous effects in this region (Black, 1997; Feng et al., 1998; Hsiao & L., 1998). Nevertheless, the previously mentioned methods are difficult to implement and they require too much computational resources. In addition, it is not easy to apply them to the different geometries when performing practical parametric studies in propeller design due to the necessary meshing process. Since the design process is 7

44 known by the iterative geometry manipulation, a simpler approach is needed. The Blade Element Momentum (BEM) theory is inherently two-dimensional and it is the less sophisticated method. However, it does not require expensive computational power when compared to CFD. In addition, the BEM theory also presents good agreement when compared with experimental data. Moreover it can be easily applied to the above mentioned iterative geometry process (Benini, 2004) making it suitable to be used during the design phase Available Propeller Design Codes Some codes suitable for the design and analysis of high altitude/low Reynolds propellers were found. Namely QPROP (Drela, 2006), QMIL (Drela, 2005b), XROTOR (Drela & Youngren, 2003) and JAVAPROP (Hepperle, 2010). QPROP, XROTOR and QMIL share the same BEM formulation described in Drela (2006). The first two are used for propeller analysis and the third is used for design with minimum induced losses using a different set of unknown variables than that used for analysis. QPROP/XROTOR major limitations are that the blade airfoil lift is assumed to be linear within the minimum and maximum lift coefficient stall limits and the post stall lift coefficients are not specified. Additionally, the drag polar of the airfoils are modelled with 2- piece parabolas within the linear lift region and an extra drag term is added if the angle of attack surpasses the stall limit. These simplifications in the airfoil performance modelling lead to a modest accuracy in the propeller performance predictions. JAVAPROP (Hepperle, 2010) propeller analysis and design code is based on the blade element momentum theory. The blade is modelled considering independent sections along the span and the formulation does not account with any three dimensional effects correction. Only four distinct airfoils can be defined along the blade and the airfoils characteristics are then interpolated in the sections between those four sections. The airfoils are modelled as pre inserted lift and drag versus angle of attack tables files making hard any iteration of the airfoils Reynolds number during the propeller design iterations or even the previous modelling of the post stall airfoils characteristics to produce the complete tables. No insight is given by the author regarding the formulation used for blade design optimization by JAVAPROP Propeller Theory Momentum Theory The simplest and classical methodology that describes a propeller working is the momentum theory, also known as actuator disk theory which was originally developed by Rankine & Froude (1889). The control volume for the momentum theory can be assumed as a stream tube that just surrounds the propeller (see Figure 2.1). This 1-D theory considers the flow as inviscid, 8

45 incompressible and irrotational. The flow enters the stream tube, is accelerated trough the rotor disk and then is exhausted from the end of the stream tube. Figure Propeller Stream-tube (Rwigema, 2010). The change in momentum of the flow along the stream-tube starting far upstream, passing through the propeller disk and just after moving off into the slipstream must be equal to the thrust produced by the propeller (Glauert, 1935). It means that the thrust produced by the propeller depends on the mass flow rate and the velocity change through the propeller. This allows the calculation of the propeller s produced thrust according to Eq. 2.1: T = m ev e m 0V Since the propeller rotates, it is possible to define its mass flow rate from continuity as: m 0 = m e = m = ρv p A 2.2 replacing Eq. 2.2 in Eq. 2.1: T = ρv p A(V e V 0 ) 2.3 Since the thrust is related to the pressure jump across the propeller disk, applying the Bernoulli s equation far upstream and downstream it becomes: T = 1 2 ρa(v e 2 V 0 2 ) 2.4 with Eq. 2.3 and 2.4 for the propeller disk velocity: V p = 1 2 (V e + V 0 ) 2.5 9

46 Thus, the airspeed through the propeller disk is simply the average between freestream velocity and final slipstream velocity. The Momentum Theory can be extended to 2D dividing the disk into annulus as shown in Figure 2.2. The increment of thrust on each annulus can be calculated as: T = ρv p 2πrΔrV e 2.6 where 2πrΔr is the area of the annulus and V p represents the induced velocity at the propeller disk and V e is the induced velocity at the far wake. Figure 2.2 Geometry of rotor annulus (Prouty, 2003). As in the original derivation of the momentum equation, it may be shown that: V e = 2V p or V xw = 2V x 2.7 where V x can be the axial or tangential flow velocity components, V a and V t respectively (see Figure 2.3). So, the annulus thrust becomes: T = 4ρπV p 2 rδr Blade Element Theory The Blade Element Theory was first developed by Drzewiecki (1892). This theory is used to determine the thrust and torque at an arbitrary radial location along the blade and it takes into account the geometry of the propeller blades, such as airfoil s shape and chord and also the incidence angle at that specific location. The blade is divided into n elementary sections along the span and it is assumed that no aerodynamic interactions occur between different blade elements. In addition, the forces on the blade elements are determined using only the twodimensional lift and drag data of the blade element airfoil according to the local angle of attack 10

47 that results from its orientation to the incoming flow. Each blade element is characterized by having a given chord and length as shown in Figure 2.3. At each element, blade geometry and flow-field properties can be related to a finite propeller thrust, dt, and torque, dq. The overall performance characteristics of the propeller blade can be obtained by integration along the radius of the blade. Figure Blade element geometry and velocities at an arbitrary radius position (Drela, 2006) Analysing Figure 2.3, the inflow angle based on the two components of the local velocity vector can be calculated as: tan φ = W a W t = V + V a Ωr V t = V(1 + a a) Ωr(1 a t ) 2.9 where: a a = V a V a t = V t Ωr also, the following relation can be obtained: W = V + V a sin φ = V(1 + a a) sin φ 2.12 The induced velocity components, V a and V t in Eq. 2.9 and in Eq are a function of the forces on the blades and are calculated through the blade element momentum theory as presented in Section The thrust produced by each elemental annulus of the disk is calculated as: dt = 1 2 BρW2 (C L cosφ C D sinφ)cdr

48 where B represents the number of the blades of the propeller. The torque produced by each element is given by Eq. 2.14: dq = 1 2 BρW2 (C L sinφ + C D cos φ)crdr Blade Element Momentum Theory Combining the previous presented theories (see Section and Section 2.5.2), it becomes possible to determine the performance of a given propeller with the known blade number, rotational speed and distributions of chord, incidence and airfoils. The blade element relative velocity and respective inflow angle are computed through the axial and tangential velocity components W a and W t. The axial velocity results from the sum of the freestream airspeed to the induced axial velocity, V a, at the propeller disk. The tangential velocity results from the sum of the velocity of the element due to the propeller rotation, with the induced tangential velocity, V t. The induced velocity components are determined from the momentum theory (see Section 2.5.1), for the annulus swept by the rotating blade element and used to calculate the angle of attack, α, as the difference between the inflow angle, φ and the incidence angle, θ. With α, the element s lift and drag coefficients can be determined from the airfoil characteristics. With these coefficients, the axial and tangential force coefficients are obtained according to the local φ: C a = C L cos φ C D sin φ 2.15 C t = C L sin φ + C D cos φ 2.16 To describe the overall propeller performance, the forces are obtained from the force coefficients according to: F x = 1 2 ρw2 cc x 2.17 where the subscript x corresponds to axial or tangential components. The total thrust and torque of the propeller are calculated by numerical integration: n T = B F a i i=1 n Q = B F t i r i= with the total torque given by Eq. 2.19, the necessary shaft power is obtained. P = ΩQ

49 and dimensionless thrust and power coefficients are calculated from their definitions: c t = c p = T ρn 2 D p P ρn 3 D p where the advance ratio is defined as: J = v nd 2.23 and the propeller efficiency is computed according Eq. 2.24: η = J c t c p 2.24 Since the induced velocity components depend on the element s forces and vice-versa, the iteration variables of the classical Blade Element Momentum method are the axial and tangential induction factors: a a = W a V V a t = Ωr W t Ωr Including their dependence on the element s force coefficients according to the results from momentum theory: a a = ( 4 sin2 1 φ 1) σ r C a 1 4 sin φ cos φ a t = ( + 1) σ r C t where σ r is the ratio of the blade element area to the annulus sweep by the element in its rotation and it is defined as: σ r = cb 2πr 2.29 Prandtl Tip and Hub Losses Corrections The original blade element momentum theory does not take into account the influence of vortices shed from the blade tips into the slipstream on the induced velocity field. However, since the blade creates a pressure difference in the flow, at the tip, that flow tends to move 13

50 from the lower blade surface to the upper blade surface, reducing the resultant force in the neighbourhood of the tip. Prandtl, as described in Glauert (1935), derived a correction factor that compensates for the amount of work that can actually be performed by the element according to its proximity to the blade s tip (it is widespread the use of this correction for the blade root too). The factor is calculated as: F = 2 π cos 1 (e f ) 2.30 where f for the tip region: f tip = B R r 2 r sin φ 2.31 Similarly to the f tip presented in Eq. 2.31, the f hub can be calculated by: f hub = B r R hub 2 r sin φ 2.32 If the element is affected by both tip losses and hub losses, the total factor is obtained by multiplying those factors. Thus, this factor F is used to modify the momentum segment of the Blade Element Momentum equations (Eq and Eq. 2.28) as presented in Eq and Eq.2.34: a a = ( 4F sin2 1 φ 1) σ r C a 1 4F sin φ cos φ a t = ( + 1) σ r C t Post Stall Models The rotational motion of the blade affects the element s boundary layer such that the airfoil stall is delayed, shifting to higher angles of attack. Besides this, the post stall behaviour of the airfoil is affected by the rotation motion condition and plays an important role in the overhaul propeller performance. In order to complement the available tools in JBLADE, and make the predictions more accurate, five models to correct the airfoil characteristics after stall were implemented. For all models presented in this subsection, except the model of Corrigan & Schillings (1994) were implemented as: c l3d = c l2d + g cl Δc l 2.35 c d3d = c d2d + g cd Δc d

51 where g cl and g cd are the functions associated with each model, while Δc l and Δc d represent the difference between the obtained lift and drag coefficients in case of no separation occurrence. The remaining c l2d and c d2d are the lift and drag coefficients measured or calculated for the airfoil. Snel et al. Model The model of Snel et al. (1994) emerged from the solution of a simplified form of the 3D boundary layer equations on a rotating blade, resulting in: g cl = 3 ( c r ) This model only changes the lift coefficient, while 2D airfoil drag coefficient is maintained unchanged. Du and Selig Model The model developed by Du & Selig (1998) is an extension of the work done by Snel et al. (1994) which accounts also for changes in drag coefficient due to the rotation of the blade. The two dimensional coefficients are modified by: g cl = 1 (c/r) [1.6(c/r)a 2π b (c/r) d Λ dr Λr R r g cd = 1 (c/r) [1.6(c/r)a 2π b (c/r) d Λ dr Λr R r 1] ] 2.39 where: ΩR Λ = 2.40 W 2 + (ΩR) 2 In their original work, Du and Selig kept the constants a = b = d = 1. The same values of a, b and d were kept herein. Although in JBLADE it is possible to change the values of these constants, to do so, the user needs to have some knowledge about their possible values. Dumitrescu and Cardos Model The model proposed by Dumitrescu & Cardos (2007) presents a correction in the lift coefficient. Similarly to the work of Snel et al. the function to correct the lift coefficient due to blade rotation came from an analysis of the momentum equations for the three dimensional boundary layer. 15

52 g cl = 1 e γ (r/c) The correction presented in Eq assumes a viscous decay of the vortex lift in the span wise direction. The authors concluded that the best comparisons with experimental data occur for γ = The same value of γ is used in JBLADE. Chaviaropoulos and Hansen Model The model formulated by Chaviaropoulos & Hansen (2000) uses a system of simplified equations which were obtained by the integration of the three dimensional incompressible Navier-Stokes equations in the radial direction of the blade. This method was extended in order to account the influence of the blade s twist. g cl = a ( c r ) h cos n (θ) 2.42 g cd = a ( c r ) h cos n (θ) 2.43 The values used in the work of Bouatem & Mers (2013) which best compare with the experimental data are: a = 2.2, h = 1 and n = 4 whereby the same values were used in the simulations of the present work. Corrigan and Schillings Model The model developed by Corrigan & Schillings (1994) correlates the stall delay to the ratio of the local blade chord to radial position. The authors analysed the pressure gradients in the boundary layer and combining with the work of Banks & Gadd (1963) they developed the correction function for the lift coefficient as presented in Eq. 2.44: c lrot = c lnonrot ( c l pot Δα) 2.44 α The function is expressed as a shift in the angle of attack as presented in Eq. 2.45: Δα = [( K (c r ) n ) 1] (α α cl max c ) 2.45 l 0 and the separation point is related with the velocity gradient, K through: ( c r ) = K

53 The authors recommend using a n value within 0.8 and 1.6. The value n = 1 proved to give good results throughout different comparisons with experimental data Propeller Momentum Theory with Slipstream Rotation The major objection to these results has been the failure of the method to account for rotation of the fluid within the slipstream. There appears to be no physical basis for neglecting slipstream rotation. Clearly, torque must be applied to turn the propeller and that torque must result in rotation of the fluid within the slipstream. Because some of the power supplied to the propeller must go to support this rotation, the propulsive efficiency will be reduced as a result of slipstream rotation. In the following analysis we shall examine the magnitude of this effect. Phillips (2002) has shown that the solution obtained from the classical propeller momentum theory (see Eq and Eq. 2.48) does not satisfy the angular momentum equation. In dimensionless form, the induced velocity from the momentum theory can be written as: V i (ω/2π) 2R tip = J C t π J with C t as defined in Eq and J as defined in Eq Following the momentum theory analysis, the propulsive efficiency for the propeller was then defined as: 1 η = TV Qω = ( C t/πj 2 ) 2.48 The author (Phillips, 2002) presented the formulae to obtain a new induced velocity (see Eq ) and the respective propeller efficiency (see Eq. 2.50) considering the slipstream rotation. V i (ω/2π) 2R tip = J2 4 + π2 4 ( C t π 3 ) J η = TV Qω = π2 4J 2 ( C t π 3) J2 1 + π2 2 J 2 ( C t π 3 ) 1 [ ] [ ] Phillips (2002) showed that the slipstream rotation increases the induced velocity and decreases the propulsive efficiency. The author states that the major difference between the induced velocity predicted from momentum theory and that predicted from vortex theory is that momentum theory predicts a zero circumferential component of induced velocity on the 17

54 upstream side of the propeller while the vortex theory accounts for that circumferential component of induced velocity Propeller Inverse Design Methodology In 1994, Adkins & Liebeck (1994) developed a new design methodology in which the momentum equations needed to be equivalent to the circulation equations. Thus, the induction factors can be related to the displacement velocity ratio, ζ, according to Eq.2.51 and Eq. 2.52: a a = ζ 2 cos2 φ (1 ε tan φ) 2.51 a t = ζ 2x sin φ cos φ (1 + ε tan φ ) 2.52 Analyzing Eq and Eq together with the geometry of Figure 2.3 the relation presented in Eq can be obtained: tan φ = (1 + ζ 2 ) x 2.53 If the condition r tan φ = const. (Betz & Prandtl, 1919) needs to be satisfied, Eq proves that ζ must be a constant independent of the radius, for a propeller shed vortex to be a minimum induced loss regular screw surface. To each new propeller design it is necessary to provide the needed thrust or shaft power. The non-dimensional thrust and power coefficients for design purposes are: P c = T c = 2T ρv 2 πr P ρv 3 πr 2 = 2QΩ ρv 3 πr which, when applied to the Thrust and Power per unit of radius result in Eq and Eq. 2.57: T c = I 1 ζ I 2 ζ P c = J 1 ζ + J 2 ζ where: I 1 = 4ξG(1 ε tan φ) 2.58 I 2 = λ ( I 1 2ξ ) (1 + ε ) sin φ cos φ tan φ

55 J 1 = 4ξG (1 + ε tan φ ) 2.60 J 2 = ( J 1 2 ) (1 ε tan φ) cos2 φ 2.61 Since ζ is constant for an optimum design, a required thrust results in the following constraints at Eq. 2.62: ζ = ( I 1 ) ( I 2 1 ) T c I 2 2I 2 I 2 P c = J 1 ζ + J 2 ζ On the other hand, if the power is specified along the design process, the constraints result as in Eq. 2.64: ζ = ( J 1 ) ( I 2 1 ) T c J 2 2I 2 I 2 T c = I 1 ζ I 1 ζ To obtain the blade geometry, each element, dr, is considered to have a known position, a given chord and a local lift coefficient. Thus, the lift per unit radius of one blade can be calculated according to: ρw 2 cc L 2 = ρwγ 2.66 where Γ is given by Eq. 2.67: Γ = 2πV2 ζf cos φ sin φ BΩ 2.67 Simplifying, it results in: Wc = 4πλGVRζ C L B 2.68 Assuming that ζ is known, the local value of the φ is also known from Eq and Eq. 2.68, becoming a function of the local lift coefficient only. The Reynolds number is calculated according to Eq. 2.69: Re = Wc ν

56 The selection of a lift coefficient from the airfoil data, allows the determination of the dragto-lift ratio and the total velocity can be calculated as presented in Eq.2.70: W = V(1 + a a) sin φ 2.70 where a a is given by Eq Even considering only one C L the blade geometry can be determined. Since α is known from airfoil data, the blade element incidence with respect to the disc can be calculated as in Eq. 2.71: θ = α + φ 2.71 This design methodology also takes into account the tip losses according to Prandtl s formulation. The formulation of the Prandtl tip losses (see Eq and Eq. 2.31) according to the inverse design methodology is described in Eq. 2.72: f = B 2 1 ξ sin φ t 2.72 where: tan φ t = λ (1 + ζ 2 ) 2.73 The inflow angle is calculated using and the tip s inflow angle, as presented in Eq. 2.74: tan φ = tan φ t ξ 2.74 Eq represents the condition in which the vortex sheet in the wake is nothing more but a rigid screw surface (r tan φ = const.). The inverse design methodology is summarized in Figure Forces acting on a Propeller When a propeller is subjected to the rotation, the interaction between the flow and the blades, and the blades mass inertial forces, causes loads and strains. Thus, twisting and bending forces appear throughout the propeller blades (AC65-12A, 1976; Curtiss-Wright, 1944). These forces and their location along the blade can be calculated with Blade Element Momentum theory presented above and the magnitude and location of the forces can then be used to calculate the blade deformations. 20

57 Read Inputs Select an initial ζ Computation of F and ϕ Computation of Wc Computation of minimum ε i = i + 1 Determination of α, c l and c d Computation of a a, a t and W Computation of β and c Yes r i No Computation of the I and J Update ζ Computation of new ζ ζ res 1e Yes No Display Blade Geometry Figure Flowchart of inverse design procedure in JBLADE. During the rotational motion, the centrifugal force acts from the hub to the tip of the blade, tending to pull the blades from the hub (see Figure 2.5 (a)). The greater the propeller rotational speed, the greater the centrifugal forces will be. The thrust bending force (see Figure 2.5 (b)) attempts to bend the propeller blades forward at the tips, because the lift toward the tip of the blade flexes the thin blade sections forward. The torque bending forces, as presented in Figure 2.5 (a) try to bend the propeller blade back in the opposite direction at which the propeller is rotating. 21

58 (a) Figure 2.5 (a) Illustration of propeller torque bending force and propeller centrifugal force. Reproduced from Mechanics Powerplant Handbook (1976) (b) Illustration of propeller trust bending force. (b) Besides the bending and centrifugal forces mentioned above, the propellers blades are also subjected to aerodynamic and centrifugal twisting moments (AC65-12A, 1976; Curtiss-Wright, 1944) Volume and Blade Mass Estimation The estimation of the blade mass was implemented and its validation is presented in this section. To calculate the volume of the blade, an integration along each station of the airfoil is performed. For the completely solid structure and for the case of the skin thickness concepts the volume of the blade is calculated as: n V Blade = A i + A i+1 2 i=1 Δr 2.75 If the blade is solid, the mass of the blade is calculated as: M blade = V Blade ρ mat 2.76 In the case of the skin thickness the mass is calculated as: where: n M blade = V Skin ρ mat 2.77 V Skin = (A ext i A int i ) + (A exti+1 A inti+1 ) Δr 2 i= If the blade concept contains a skin and an additional core material, the blade volume is calculated as: 22

59 V Blade = V BladeSkin + V BladeCore 2.79 where and n V BladeSkin = (A ext i A int i ) + (A ext i+1 A inti+1 ) 2 i=1 Δr 2.80 n V BladeCore = A core i + A core i+1 2 i=1 Δr 2.81 To calculate the blade mass it is just needed to simply multiply the volume by the density of the desired material. For the cases where the blade is solid or just have a skin, the blade mass is calculated as: M Blade = V Blade ρ mat 2.82 If the third concept is chosen, then the blade mass is calculated as: M Blade = V Bladeskin ρ matskin + V Bladecore ρ matcore Blade Bending Estimation To calculate the blade s tip displacement due to the normal force produced in the propeller s operation, it was necessary firstly to calculate the inertia modulus of each airfoil section. The second moments of area were obtained according: I xx = y 2 A I yy = x 2 A da 2.84 da 2.85 In order to simplify the simulations, it was considered a simple cantilevered beam (see Figure 2.6), with the constraint located at the root and the forces applied at 25% of the chord, in order to produce a pure bending moment. Figure 2.6 Scheme of a cantilevered beam with a group of arbitrary positioned loads. 23

60 In order to calculate the angle and the displacement at each element of the blade, it is necessary to determine the bending moment at each element. The bending moment was calculated according to Eq : n(x) M (x) = M 0 P i x i i= Then, the angle and the displacement at each element of the blade were calculated according to Eq and Eq. 2.88, respectively. θ i = θ i 1 M (x) EI (x) Δx δ i = δ i 1 + θ i 1 Δx M (x) 2EI (x) Δx In the cases that the blades are composed with more than one material, like the case Skin + Core Material, the equivalent bending stifness is determined according to: EI (x) = E 1 I 1(x) + E 2 I 2(x) Blade Twist Deformation To calculate the twist deformation during propeller operation, the concept illustrated in Figure 2.7 was used. The twisting moment T, was calculated according to the next steps: The angle of attack at each blade section was computed, in JBLADE s aerodynamic sub-module. The airfoil s pressure centre location computed during XFOIL calculations was used and the distance between this pressure centre and the section s 25% chord was determined. The Moment is calculated by multiplying the Force previously computed in JBLADE aerodynamic sub-module and the distance calculated above. Figure 2.7 Illustration of a beam subjected to a twisting moment. 24

61 The torsion angle can be calculated according to Eq. 2.90: T x θ i = θ i 1 + JG where according to Young et al. (2002) J can be defined as: J s = 4I xx I xx Ac Present Research Contributions to Propeller Aerodynamics Modelling New 3D Flow Equilibrium Model The theoretical formulation presented in Section assumes that the flow in the propeller annulus is two-dimensional, meaning that radial movement of the flow is neglected. However, for such condition, three-dimensional equilibrium must exist as discussed in Section for the Momentum Theory. Furthermore, the classical Blade Element Momentum formulation assumes that neighbouring blade elements induced velocities are independent, which lacks physical reasoning (Wald, 2006). In JBLADE (see Figure 2.3) this issue is addressed by a new model based on 3D flow equilibrium, as presented by Saravanamuttoo et al. (1996) considering that before the propeller disk, the enthalpy is radially uniform across the flow and the entropy gradient is null as well: 2 W a W a r + W V t t r + W t r = where W a is the axial flow velocity across the disk, V t is the tangential flow velocity in the disk and r is the radial position in the disk. The case where W a is maintained constant across the propeller annulus, reduces Eq to Eq. 2.93: dw t dr = W t r W tr = const In this case, the whirl varies inversely with radius, which is best known as the free vortex condition. Although this differs substantially from the ordinary BEM approach, where the momentum theory applied to the tangential velocity induction totally disregards the neighbour elements to determine the element s V t, it makes sense when one considers that from far upstream down to the propeller disk, the flow should be isentropic or close to irrotational, thus 25

62 respecting the free vortex condition. To implement this equilibrium condition, in the first iteration the forces coefficients are computed assuming no tangential induction factor, which means that a t = 0. The mass flow rate at an arbitrary annulus element i and total mass flow rate are calculated as presented in Eq and Eq respectively. m i = 2ρW a πrdr 2.94 R m total = m i 2.95 R hub To satisfy the momentum conservation, the total propeller torque will be the result of a free vortex induced tangential velocity profile with an average axial velocity, W a across the propeller disk. A reference value of tangential induced velocity is used that corresponds to that at 75% of the blade radius, V t75. The average axial velocity is calculated according to: W a = m total πρr At a given element V t is calculated as: V t = 0.75R V t 75 r 2.97 The total torque of the blade can be calculated as presented in Eq. 2.98: Q = 4πρW av t rdr 2.98 Thus, replacing Eq and Eq.2.97 in Eq.2.98 and solving for V t75, we get Eq. 2.99: V t75 = 2 3 Q πρw ar(r 2 2 R hub ) 2.99 The tangential induction factor can be updated and the coefficients will be calculated again with the updated tangential induction factor. a t = V t Ωr New Methods for CD 90 Prediction Sometimes, the data required for rotary wing performance estimation codes need to be extrapolated from the available wind tunnel data (Worasinchai et al., 2011). In addition, during the extrapolation process one of the aspects with major weight, as referred by Montgomerie (1996), is the airfoil drag coefficient at an angle of attack of 90 degrees. The developments to 26

63 predict the drag coefficient at 90 degrees began with Gault (1957), who presented the low speed stalling characteristics of airfoils and correlated them with a single specific upper thickness coordinate located at x/c = The results presented by Gault are restricted to airfoils without high-lift devices and to airfoils with aerodynamically smooth surfaces, and he considered also the Reynolds number influence on airfoils stalling characteristics. Later, in 1995, Montgomerie (1996, 2004) presented two different methods to predict the value of the drag coefficient and its distribution along a wind turbine blade. The first method considers a constant drag coefficient distribution along the entire blade and represents the most widely used method by wind turbine manufacturers. The second method consists of a curvilinear distribution of drag coefficient at 90 degrees. In 2000, Lindenburg (2000) presented an empirical relation to calculate C D90 based in a similar approach used by Montgomerie. To make valid the assumption that the airfoil acts as a flat plate in the 90 degrees angle of attack condition, Lindenburg assumed that the flow on one side of the airfoil is fully separated. Recently, Timmer (2010) presented a correlation to predict the value of drag coefficient at 90 degrees based on Gault s approach. He correlated the same airfoil coordinate, (y c) x/c=0.0125, with experimentally measured drag coefficients at 90 degrees and presented a linear correlation for drag coefficient prediction at 90 degrees. Initially, the method described by Montgomerie (2004) was used in JBLADE, but it was found that different extrapolated 360 degrees polars will lead to significant differences on final predicted power and thrust forces (see Figure 3.21) for the same propeller. Airfoil Leading Edge Radius Method In this new proposed method, CD 90 is correlated with the airfoil leading-edge radius. The leading-edge radius of an arbitrary airfoil was calculated using an approximation by the leastsquare method on its set of contour coordinates. For a NACA four-digit-series airfoil, it is possible to calculate the leading-edge radius through: R LE = t The leading-edge radius was calculated for different NACA airfoils, and the results are presented in Table

64 Table Leading edge radius calculations and errors due to the least square method approximation Airfoil Name LE Radius LE Radius w/ Least w/ Eq Square Method Error, % NACA NACA NACA NACA NACA NACA NACA The greatest difference occurs for an airfoil with 9% thickness, and it is 3.75%, which is a reasonably low value. The drag coefficient at 90 degrees of specific airfoils was then calculated (see Table 2.2) and plotted against their experimentally measured values of drag coefficient at 90 degrees, as presented in Figure 2.8. The linear correlation that was found to fit the data is: C D90 = LE Radius Figure Measured airfoil drag coefficient at 90 degrees AoA vs airfoil leading edge radius. The airfoil data correspond to those of Table 2.2. Airfoil ( y ) at x = Method c c An improvement to the fitting previously presented by Timmer (2010) was also implemented. The airfoil y coordinate at x/c = for more airfoils (see Table 2.2) was calculated and airfoils were added to the originally considered database. The comparison between new and original correlations can be observed at Figure 2.9. This new correlation was also implemented in the JBLADE software providing a second option for the calculation of C D90. 28

65 Figure Comparison between original correlation, described by Timmer (2010) and improved correlation. The airfoil data correspond to those of Table 2.2. The new correlation obtained with the y coordinate at x/c = is given by: C D90 = ( y c ) ( x c =0.0125) Table 2.2 Drag coefficient at 90 degrees measured and calculated by the two developed methods for a set of airfoils. Airfoil Name Reference Measured CD 90 Calculated CD90 w/ LE Radius Calculated CD90 w/ y/c ( x c )= DU 91-W2-250 (Timmer, 2010) DU-97-W-300 (Timmer, 2010) FX 84-W-127 (Massini et al., 1988) FX 84-W-218 (Massini et al., 1988) LS-417 (Timmer, 2010) LS-421-MOD (Massini et al., 1988) NACA 0012 (1) (Lindenburg, 2000) NACA 0012 (2) (Massini et al., 1988) NACA 0012 (3) (Timmer, 2010) NACA 0015 (Miley, 1982) NACA 0018 (Timmer, 2010) NACA 4409 (Ostowari & Naik, 1984) NACA 4412 (Ostowari & Naik, 1984) NACA 4415 (Ostowari & Naik, 1984) NACA 4418 (Ostowari & Naik, 1984) NACA (Massini et al., 1988) NACA (Massini et al., 1988) NACA (Lindenburg, 2000) NACA (Lindenburg, 2000)

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67 Chapter 3 JBLADE Software Development JBLADE is a numerical open-source propeller design and analysis software written in the C++/QML programming language, compiled with Qt toolkit (Digia, 2014). The code is based on QBLADE (Marten & Wendler, 2013; Marten et al., 2013) and XFLR5 (Deperrois, 2011) codes. It uses the classical Blade Element Momentum (BEM) theory modified to account for 3D flow equilibrium. The airfoil performance figures needed for the blades simulation come from the XFOIL (Drela, 1989) sub-module. This integration, allows the fast design of custom airfoils and computation of their lift and drag polars. The software can estimate the performance curves of a given propeller for off-design analysis. It has a graphical user interface (GUI) making easier the task of designing the propeller and analysing the simulations. The long term goal of JBLADE is to provide a user-friendly, accurate, and validated open-source code that can be used to design and optimize propellers for a large spectrum of applications Software Overview Figure 3.1 shows the JBLADE software structure with the different sub-modules and their iteration routines in which the airfoil polars, blades, propellers and simulations are defined, executed and stored. Furthermore, it can be seen how the BEM module is coupled with the XFOIL sub-module. JBLADE software allows a direct visualization of simulation results through a GUI making the software accessible and easy to understand by willing users. In addition, the coupling between different JBLADE modules avoids time consuming operations of importing/exporting data, decreasing possible mistakes created by the user. The simulation starts by importing the blade s sections airfoils coordinates into the XFOIL sub-module. A direct analysis for each airfoil performance over the largest possible angle of attack range is performed. These XFOIL airfoil performance polars are used in the 360º Polar Object, where a full 360º range of angle of attack airfoil polar for each blade section airfoil is built. Each 360º polar is defined by its name and parent XFOIL polar. After at least one 360º Polar is stored in 31

68 the 360º Polar Object database sub-module, a blade can be defined in the Blade object submodule. This sub-module stores the blade s geometric data as well as which 360º polar is associated to each of the blade sections previously defined in the Blade Object. After the creation of the blade, a propeller can be defined in the Propeller Object sub-module. This submodule is used to store the propeller data as well as the simulation parameters associated to each propeller. The simulation results, which characterize the propeller performance are obtained in the BEM simulation sub-module and stored in the Blade Data Object sub-module for each element along the blade and added to the Propeller Simulation Object database. Airfoil Design Airfoil Analysis -Coordinates; -Airfoil Camber; -Airfoil Thickness; -Lift and drag coefficients; -Reynolds number; -Angle of attack range. Airfoil Analysis Results XFOIL Panel Simulation - Angle of attack Range 360º Polar Extrapolation 360º Polar Extrapolation -Lift and drag coefficients; -Reynolds number; -Full angle of attack range. Extrapolated Data Blade Design and Optimization -Geometric parameters; -Number of stations; -Number of blades; 360º Polar Extrapolation Propeller Definition Sub-Module -Propeller Parameters; Blade Design BEM CODE Blade Data Object -Simulation Results data along the blade. -Induction factors; -Inflow angles; -Circulation; -Advance ratio; -Speed. Propeller Simulation Sub- Module -Simulation Parameters. Propeller Object Blade Data Object BEM Simulation -Advance Ratio; -Speed Range. Figure JBLADE software structure representing the internal sub-modules interaction Airfoil design and analysis To perform a new propeller design or performance analysis it is necessary to import the needed airfoils that will be used along the blades sections. Subsequently, the performance of the airfoils should be computed over the largest angle of attack range. The XFOIL (Drela, 1989) 32

69 code is used to compute and analyse the flow around the airfoils. The XFOIL most relevant features for JBLADE are the inviscid/viscous analysis of an airfoil with forced or free transition. In addition, the XFOIL capacity to calculate transitional separation bubbles and predict the airfoil performance just beyond the stall make the code helpful and useful in JBLADE (Drela, 1988). In order to obtain accurate results with JBLADE software, it is essential that the correct Reynolds and Mach numbers are defined in the airfoil simulation settings (see Figure 3.2). The achievement of correct Reynolds and Mach numbers along the blade may take some iteration until the propeller analysis process is finished. The XFOIL sub-module allows the simulations for a given Reynolds number over an angle of attack (AoA) range and the simulation for a given angle of attack over different Reynolds numbers. In addition, depending on the number of the points of an imported airfoil, a global refinement of the airfoil s panels is needed to ensure good convergence during the airfoil analysis. Furthermore, the XFOIL sub-module allows direct modifications of the airfoils by changing the airfoil thickness and its position as well as airfoil camber and its position. Regarding the inverse design capabilities of this sub-module, it maintains all the functionalities originally developed for XFLR5 (Deperrois, 2011). Each time that one of the previous mentioned parameters is modified a new airfoil will be generated. Figure XFOIL sub-module in JBLADE. Figure 3.2 shows the settings that user needs to define in a typical airfoil simulation in JBLADE. The data obtained in this XFOIL sub-module will be used in the 360º Polar Extrapolation submodule, where a full 360º range of angle of attack airfoil polar for each blade section airfoil will be built º AoA Polar extrapolation Since the propeller blade sections can achieve high angles of attack during their operation, the available airfoil performance data need to be extrapolated to become available for the full 33

70 360º of angle of attack. In this sub-module the previously calculated data for each airfoil is extended to the full range of angle of attack (see Figure 3.3). As shown in Section different values of drag coefficient at 90º of angle of attack may lead to different extrapolated airfoil polars, which in turn, will lead to different propeller performance prediction. Originally, the method described by Montgomerie (2004) was used in JBLADE, but, later, the methods described in Section were integrated. These methods proved to improve the extrapolation process leading to a decrease of the errors introduced by the user. The polars calculated in XFOIL sub-module can be selected in the drop-down menu and an extrapolation can be conducted. The Montgomerie's (2004) extrapolation procedure uses a blending function to make the transition between the XFOIL prediction curve and the flat plate curve. In this procedure the user can modify the resulting coefficients modifying the sliders present in this sub-module (see Figure 3.3). Additionally, the user should specify the 2D drag coefficient of the airfoil at 90º. The complete extrapolation procedure of airfoils polar extrapolation is described by Montgomerie (2004). The Viterna & Janetzke (1982) extrapolation procedure consists on empirical equations. In this procedure the user should specify the aspect ratio of the future blade as described in the work of Viterna & Corrigan (1982). In addition, there are 2 more methods available to extrapolate the airfoil polars to 360º of angle of attack. Both LE Radius and Y Coordinate are based in Montgmerie s extrapolation process. In the LE Radius option, the C D90 is calculated as described in Section while in the Y Coordinate the airfoil C D 90 is calculated as presented in Section The polars generated in the 360 Polar Extrapolation sub-module will be used in the propeller performance calculations. Furthermore, these polars data will be used also to determine the drag-to-lift ratio in the Inverse Design sub-module. Figure Polar Extrapolation Sub-Module Screen Blade definition The JBLADE software allows the introduction of the blade geometry as an arbitrary number of sections characterized by their radial position, chord, twist, airfoil and airfoil s associated 360 AoA polar. The user should specify the number of blades and the hub radius of the propeller. 34

71 The software provides a 3D graphical representation of the blade/propeller to the user (see Figure 3.4), helping the user to identify possible issues, e.g. a conflict between blades at root region if the hub radius is too small for the root section chord. Furthermore, this sub-module allows the blade s geometry exporting to use in a conventional CAD software. Whenever a blade is deleted or overwritten, all associated simulations and propellers are deleted as well. Figure Blade Definition Sub-Module Propeller inverse design The propeller inverse design methodology was implemented in JBLADE as presented in Section The user should specify the operating condition of the propeller, namely air density in which the propeller will operate, the free stream speed, the propeller rotational speed and the power (or torque) delivered to the propeller or thrust produced by the propeller. To use the inverse design tool, the user should previously specify the number of blades, the blade hub radius, the radial position of each station, as well as station s airfoil and its associated polar (see Figure 3.5). After the introduction of these parameters, the inverse design procedure (see Figure 2.4) is applied and the on-design optimal blade geometry is achieved. In addition the user should specify the criteria to minimize the drag-to-lift ratio. There are 3 options available: specify a constant C L over the blade or specify the airfoil s best L 3/2 /D or airfoil s best L/D. After the inverse design procedure, the obtained blade can be saved and used normally in the Simulation sub-module. 35

72 Figure Blade definition/inverse design sub-module in JBLADE Parametric simulation In the Parametric Simulation sub-module the propeller can be simulated using a multiparameter simulation. This sub-module (see Figure 3.6) allows simulations by defining the interval and incremental values of the propeller operational parameters speed, rotational speed and pitch angle. These variations in different parameters allow performing parametric studies of the propeller. Whenever a simulation is defined, all simulation parameters need to be specified. For analysing the results of the simulations, the four graphs show the simulation results. By double-clicking on a graph, it is possible to change the plotted variables and by right-clicking on a graph, is possible to change the graph type. Figure 3.6 Parametric Simulation Sub-Module in JBLADE. 36

73 Propeller definition and simulation In the Propeller Definition and Simulation sub-module the user can create new propellers composed by the previously defined blades (see Figure 3.7). This sub-module allows simulations within a speed interval, for a fixed rotational speed and fixed pitch angle. To define a new propeller simulation the user should specify the propeller rotational speed and the minimum and maximum free stream speeds to be calculated. Each propeller can have more than one associated simulations. To create and perform the simulation for a given propeller, the user should specify the number of elements along the blade, the convergence criteria, the density and viscosity of the fluid and maximum number of iterations (see Figure 3.9). The propeller performance estimation is then obtained with a BEM simulation routine (see Figure 3.8) and stored in the blade data object (see Figure 3.1) for each element along the blade. Furthermore, the user can improve the accuracy of the simulations using other tools also available in the JBLADE software (see Figure 3.9) such as: Root and Tip Losses (see Section ), Post Stall Models (see Section ), Foil Interpolation (see Section ), 3D Equilibrium (Morgado et al., 2015) (see section 2.4.1) and Reynolds Drag Correction (see Section ) (Marten et al., 2013). Figure 3.7 Simulation sub-module overview. When 3D Equilibrium formulation is enabled the formulation presented in Section is applied and an initial layer of iteration in which a t = 0 appears. After solving this additional iteration layer, the radial induction factor can be updated and the coefficients will be calculated again with the updated radial induction factor. This sub-module also allows the comparison between different propellers and between different simulations for the same propeller as well. 37

74 Read Simulation Parameters For each speed For each blade element Initialization of a a and a t Computation of φ Computation of α Determination of c l and c d k=k+1 Computation of new a a and a t j=j+1 a k+1 a k < ε No i=i+1 Yes r Yes No Compute c t, c p, η and J W i W final Yes No Display Results Figure Flowchart of simulation procedure in JBLADE. Figure Simulation definition dialog box. 38

75 Number of blade elements As mentioned in Section each blade is composed by an arbitrary number of sections that are introduced by the user. Additionally, the blade is divided in elements, sinusoidally spaced along the blade s span and used to perform BEM calculations. The number of elements represents the divisions that will be used during the simulation procedure and is independent of the blade s sections number (see Figure 3.10). The elements are sinusoidally spaced along the blade, ensuring a smooth change between the elements parameters all over the blade radius. When an analysis is being performed, the BEM algorithm is executed once for every element. The input values of chord and twist are interpolated between the blade sections, where they were previously defined, and computed for the centres of each element. All the variables used in the BEM simulation are computed for the centre of each element and are treated as the average values over the element. Figure 3.10 Representation of the sections and the sinusoidal spaced elements along the blade. Foil interpolation A linear interpolation of the section parameters between the two closest sections with defined airfoils is available. When the Foil Interpolation is selected, the polar data used for the BEM s calculations of each element is a linear interpolation between the polar data of the bounding Sections airfoils (see Figure 3.10). If the Foil Interpolation is not selected, all blade elements laying between position 1 and 2 are linked to the airfoil polar data from Section 1. Thus, the last airfoil at Section n, is not included in the simulation. Furthermore, a discontinuity between the elements may appear, since the airfoil in Section 1 can be different from the airfoil in Section 2 and thus they may have different performances. Although the linear interpolation between two airfoil polars never represents the true behaviour of the intermediate elements, the interpolation represents a better approximation to the real polar on the intermediate elements. 39

76 Fluid density and viscosity The fluid density is used to calculate the power and thrust of the propeller, while the dynamic viscosity of the flow is needed to compute the local Reynolds number along the blade according to Eq. 3.1: Re r = W rc r ρ μ 3.1 Convergence criteria The convergence criterion ε conv defines when the iteration has converged and it is used to stop the iteration on that element. The convergence is achieved when the difference between actual and last iteration induction factors are smaller than the convergence criterion. The user should specify the value for ε conv that is defined as presented in Eq max( a a a a old, a t a told ) ε conv 3.2 Relaxation factor A common problem during the iteration loop of a BEM computation is the fluctuating behaviour of the axial induction factor (Marten & Wendler, 2013). This may lead to a stop of the iteration after the maximum number of iterations is reached and impacts both on the code s performance and accuracy. The relaxation factor is introduced in the iteration after a new value, a k+1, for the axial induction factor has been calculated: a k+1 = ω relax a k+1 + (1 ω relax )a k 3.3 Reynolds Number Correction The changes in lift and drag polars due to Reynolds number effects are not included in JBLADE. The polars are always computed for a fixed Reynolds number. During the simulation of a propeller, the Reynolds number is changing for every operational point. The user should carefully check how large the deviation is for each case. Hernandez & Crespo (1987) suggested a correction in which the lift polar remains unchanged and the drag polar is corrected by scaling the drag coefficient inversely with the Reynolds number. c D = c DRef ( Re Reexp Ref Re )

77 Structural sub-module In the Structural sub-module (see Figure 3.11) the user can create new materials that will be used to perform the structural analysis to the propeller s blades. Furthermore, the structural analysis can be defined in this sub-module as well. It is possible to estimate the mass of the blade according to the previously defined blade s material. In addition, it is possible to calculate the tip displacement, due to the thrust produced by the propeller, and the torsional deformation, due to aerodynamic twisting. Figure 3.11 Structural sub-module overview. Creating and editing materials To define a new material (see Figure 3.12), the user should specify the name, the density and the Young Modulus. After defining these properties, the material is added to the Material database and stored. In addition, each material can be modified or deleted. To maintain the software s consistency, when a material is deleted, all the structural simulations using that specific material are deleted as well. Figure 3.12 New material definition dialog box. 41

78 3.2 - JBLADE Software Validation Propeller Geometries The data from NACA Technical Reports (Gray, 1941; Theodorsen et al., 1937) were used to validate the simulation procedures, the methodologies presented in Sections up to 2.6 and in Section 2.9 and also the Software performance predictions. The propeller presented by Adkins & Liebeck (1994) was used to validate the inverse design methodology (see Section 2.5.5) as well as the JBLADE performance predictions. The APC 11 x4.7 propeller was also used to validate the JBLADE aerodynamic predictions. NACA Technical Report 594 The propeller used to validate JBLADE Software corresponds to the NACA Technical Report No. 594 (Theodorsen et al., 1937) configuration Nose 6 Propeller C. The propeller has 3 blades and a diameter of m (see Figure 3.13(a) and (b)). (a) Figure NACA Technical Report No. 594 (Theodorsen et al., 1937) propeller (a) propeller geometry (b) propeller visualization in JBLADE. (b) NACA Technical Report 530 The propeller 6267A-18 presented in NACA Technical Report No. 530 (Gray, 1941) uses the Clark Y airfoil along the entire span. This propeller was originally tested with a meters diameter spinner with a rotational speed of 520 RPM. The propeller has 3 blades and a diameter of m. Its geometry and visualization are represented in Figure 3.14 (a) and (b), respectively. 42

79 (a) Figure NACA Technical Report No. 530 (Gray, 1941) 6267A-18 propeller (a) propeller geometry (b) propeller visualization in JBLADE. (b) Adkins and Liebeck Propeller The propeller presented by Adkins & Liebeck (1994) has 2 blades and a diameter of 1.75 m. The propeller s section consists of NACA 4415 airfoils from root to tip. The blade geometry is presented in Figure 3.15 (a) and its visualization inside JBLADE is presented in Figure 3.15 (b). (a) Figure Propeller geometry presented by Adkins & Liebeck (1994) (a) propeller geometry (b) propeller visualization in JBLADE (b) APC 11 x4.7 The APC 11 x4.7 propeller was also used to validate JBLADE for low Reynolds number predictions. The propeller was replicated according to the data found at UIUC Propeller Database (Brandt et al., 2014). Figure 3.16 (a) shows the chord and pitch angle distribution 43

80 along the blade radius. The propeller has 2 blades and 0.28 m of diameter, and when replicated in JBLADE it becomes as in Figure 3.16 (b). (a) Figure APC 11 x4.7 propeller(brandt et al., 2014) (a) propeller geometry (b) Illustration of the propeller inside JBLADE (b) Simulation Procedure Validation With the presented architecture of the JBLADE Software, a simulation using the propeller described in Section was conducted. To start the simulation procedure the airfoil polars were obtained in the XFOIL sub-module. The polars were then extrapolated such that the lift and drag coefficients became available for post stall angles of attack. Geometry presented on Figure 3.13 (a) was replicated in order to define the propeller blades in JBLADE and the corresponding airfoil for each blade section was used, obtaining the propeller represented at Figure 3.13 (b). The blade pitch angle was adjusted to the given angle at 75% of the radius and the propeller performance was computed. In order to understand how to perform a correct propeller simulation in JBLADE, the number of points necessary to define an airfoil was studied. This procedure allows the optimization of the XFOIL numerical accuracy and the different polars obtained with different number of points are presented in Figure 3.17 (a). It can be observed that, for more than 200 points XFOIL does not show a significant difference in the airfoil polars. Thus, in the simulations performed along this thesis each airfoil was refined in order to have, at least, 200 points. Since each section of the blade has a specific Reynolds and Mach number, the capability to correctly predict the airfoil performance plays a key role on the propeller analysis, a study was also conducted and the results are presented in Figure 3.17 (b). It can be concluded, as the existing literature suggests (Selig, 2003), that XFOIL can correctly predict the airfoil performance for Reynolds and Mach numbers intervals of interest to high altitude propellers. 44

81 Therefore, since the capability of XFOIL correctly predicts the airfoil performance, a detailed study was conducted and is described in Chapter 4. (a) (b) Figure 3.17 E387 airfoil polars. (a) Validation of polar calculation using different number of points to define the airfoil in XFOIL (b) Comparison between XFOIL and experimental studies (Selig & Guglielmo, 1997) different Reynolds numbers To correctly replicate the geometries presented in both NACA Reports, a search was conducted to find how the blade pitch angle was measured in the original NACA Reports. However, there are no clear indications about how the blade angle was measured at each radial position. Analysing the two common reference lines (see Figure 3.18), it was concluded that NACA tests refer to the lower surface of the blade, the usual practice at that time. Regarding the difference on a Clark Y airfoil having 12% thickness it becomes: θ Axis θ LowerSurface Since JBLADE considers the pitch angle equivalent to the θ Axis, these extra 2º were thus added to the geometries from NACA Reports to ensure the agreement between the tests and the JBLADE simulations. This procedure was also adopted by other authors as presented by Hepperle (2010). 45

82 Figure Possible reference lines for blade pitch angle measurements. To validate the computations for a wide range of advance ratios, independent simulations for small, medium and large advance ratios were performed and compared with the previously calculated curve using the average distribution of Reynolds and Mach numbers along the blade (see Figure 3.19). For each of the blade s defining section the average Reynolds and Mach number was set as the mean value corresponding to half the advance ratio that corresponded to the propeller operating conditions used to collect the experimental data. The propeller rotational speed was constant at 1800 RPM. The VMIN points were obtained with the distribution of Reynolds and Mach numbers for a low advance ratio operating condition. The airfoil polars were calculated using the Reynolds and Mach number distribution for the advance ratio about 0.1 and the propeller performance was only analysed for this specified advance ratio. The COMPUTED curves were calculated with the Reynolds and Mach numbers distributions for an intermediate advance ratio, close to the maximum efficiency of the propeller. The VMED simulations were performed using the same Reynolds and Mach numbers as the COMPUTED curves. The VMAX points were obtained with the same procedure but for an advance ratio close to the zero thrust condition of the respective propeller. Observing Figure 3.19 it is possible to conclude that the averaged Reynolds and Mach numbers distribution VMED, which correspond to an intermediate advance ratio, allow a close approximation for the full range of advance ratios simplifying the simulation procedure. In addition, the influence of the improvements made on the theoretical formulation of JBLADE were studied and the results can be observed in Figure The Original BEM curve corresponds to the initial formulation described in Section and, as it was incorporated in QBLADE for wind turbines but here extended to simulate propellers. The Mod. BEM curve corresponds to the modification of the classical BEM with the 3D Equilibrium described in Section Analysing Figure 3.20, it can be observed that the 3D Equilibrium implementation had resulted in significant improvements throughout the complete advance ratio range. 46

83 (a) (b) (c) Figure Validation of calculations for the Propeller C of NACA TR 594 (Theodorsen et al., 1937) using a distribution of averaged Reynolds and Mach Numbers along the blade: (a) thrust coefficient (b) power coefficient, (c) propeller efficiency. The Mod. BEM + Post Stall curve includes the post stall model described in Section Since there are different post-stall models available, the selection of the adequate post-stall model was studied and the results are presented in Section Figure 3.20 shows that the best performance prediction is obtained using the post-stall model together with 3D Equilibrium. Thus, the simulations throughout this thesis were performed using the post-stall model (Corrigan & Schillings, 1994) and 3D Equilibrium. 47

84 (a) (b) (c) Figure Modelation influence on the simulated propeller performance: (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 48

85 Methods for Drag Coefficient at 90º Prediction Validation A new method for predicting the drag coefficient at an AoA of 90º was described in Section In order to evaluate the improvements in the propeller performance prediction of the new proposed method for the C D90 calculation, additional simulations of the propellers presented in Section and Section were performed. The results are presented and discussed below. Since both methodologies lead to close predictions for the drag coefficient at 90 degrees, the simulations were only performed with the method that correlates the airfoil s drag coefficient at 90 degrees with the airfoil s leading edge radius. NACA Technical Report 594 The procedure described in Section was applied in order to obtain the propellers performance predictions. The curve JBLADE C D90 = 1.4 presented in Figure 3.21 represents the initial formulation as it was incorporated in QBLADE (Marten et al., 2013) for wind turbines but extended here to simulate propellers. These curves were obtained with a constant value of drag coefficient as suggested by Montgomerie (1996) in his first method. According to this method, the value of, C D90 = 1.4 was used for all airfoils from root to tip of the blades. Figure 3.21 (a) and Figure 3.21 (b) show that this methodology underpredicts the propeller s thrust and power coefficients, especially in the lower advance ratio region. The curves JBLADE Improved Polar correspond to the modified polars extrapolation, as described in Section These solid lines were obtained with the method in which the CD 90 is correlated with the airfoil s leading edge radius. Observing Figure 3.21 (a) and (b) it is possible to conclude that this methodology represents the closest prediction of the propeller performance over all advance ratios range for the thrust coefficient. The power coefficient is still underpredicted, but an improvement is observed when compared to the JBLADE CD 90 =1.4 The curves JBLADE C D90 = 2.2 follow the same procedure as presented for the curve JBLADE C D90 = 1.4 modifying only the value of the C D90 from 1.4 to 2.2. This value of C D90 lead to an over prediction of the thrust coefficient (see Figure 3.21(a)) in the lower advance ratio region. Regarding power coefficient (see Figure 3.21 (b)), its prediction becomes closer to the experimental data but still under predicted. Since the proposed method modifies the value of drag coefficient at 90 degrees AoA to a more reasonable value, it changes the extrapolated 360º AoA airfoil drag coefficient polar and consequently improves the propeller performance prediction. It is seen that the CD 90 and the complete 360º AoA range airfoil polars play an important role in the predicted performance with a visible improvement in the thrust and power coefficients, especially at low advance ratios region. 49

86 (a) (b) (c) Figure 3.21 Influence of the 360 polars extrapolation in the propeller performance and comparison with data from NACA TR 594 for θ 75=45 : (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 50

87 NACA Technical Report 530 Figure 3.22 shows the results for the reference propeller pitch angles of θ 75 = 30. Observing the thrust coefficient results (see Figure 3.22 (a)) no significant differences are observed between the improved and previous CD90=1.4 models for this particular test case, and both seem to diverge from the experimental results as the advance ratio reduces to the lower limit. (a) (b) (c) Figure Influence of the 360 polars extrapolation in the propeller performance and comparison with data from NACA TR 530 for θ 75=30 : (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 51

88 Figure 3.23 presents the comparison between both methodologies for the propeller from NACA TR 530 but with θ 75 = 40. Both thrust and power coefficients (see Figure 3.23 (a) and (b)) predicted using the method that correlates the airfoil leading edge with the CD 90 are closer of the experimental data than the predictions obtained with the method of constant CD 90. The difference is more pronounced in the small advance ratios region and practically does not exist for advance ratios bigger than 0.8. (a) (b) (c) Figure Influence of the 360 polars extrapolation in the propeller performance and comparison with data from NACA TR 530 for θ 75=40 (a) thrust coefficient (b) power coefficient, (c) propeller efficiency. 52

89 However It should be noted that from TR530 it is clear that the abrupt reduction of the c t and c p values occurring at low advance ratio is then reversed as the advance ratio lowers even more. So, the apparent divergence may not really exist. On the other hand, for such a low pitch setting of 30º, both models underpredict the peak efficiency values, although the improved model behaves slightly worst than the previous model. The power coefficient (see Figure 3.22 (b)) also shows no significant differences between both methods and experimental data. Figure Influence of the 360 polars extrapolation in the propeller performance and comparison with data from NACA TR 530 for θ 75=50 (a) thrust coefficient (b) power coefficient, (c) propeller efficiency. 53

90 Figure 3.24 presents the comparison between both methodologies for the propeller from NACA TR 530 but with θ 75 = 50. Observing Figure 3.24 (a) it is possible to conclude that the method that correlates the airfoil leading edge with the CD 90 is overestimating the thrust coefficient, with the method of constant CD 90 is giving the best results for this specific case. Figure 3.24 (b) shows that the new proposed method improves the estimation of the power coefficient for this specific propeller, especially in the smaller advance ratios region Post-Stall Models The post-stall models described in Section were implemented in JBLADE and the propellers from NACA Report No. 594 were also used to evaluate the post-stall models behaviour and improvements when compared to the original BEM formulation. NACA Technical Report 594 Figure 3.25 (a) shows that all the implemented models improve the thrust coefficient prediction when compared with a simulation in which no post-stall was used ( Original BEM curve). The models show small discrepancies between the experimental and predicted thrust coefficients. Figure 3.25 (b) shows the effect of the post-stall models in the power coefficient prediction. Contrary to the thrust coefficients prediction, the power coefficient is significantly under predicted, even with the post-stall models correction. For both, thrust coefficient and power coefficient it is shown that the effect of the post-stall models is more pronounced on the low advance ratios regions. It was found that for this case the model developed by Corrigan & Schillings (1994) performs best over the range of conditions studied, but still exhibited some limitations, especially in power coefficient prediction as mentioned. For the case of θ 75 = 45 (see Figure 3.26 (a) to (c)), it was decided not to perform the simulations with the BEM Original theory, since the results will be worst, when compared with the results obtained using the post-stall models. Different models are predicting significantly different thrust coefficients which happens once each model changes the lift coefficient in a different way and as the higher the angle of attack, the higher are the differences on the lift coefficient at each blade s section. Besides the Dumitrescu & Cardos (2007) and the Corrigan & Schillings (1994) models, the other post-stall models tend to overestimate the thrust coefficient (see Figure 3.26 (a)). The difference seen between the predictions and the real propeller performance at low advance region on Figure 3.25(b) and on Figure 3.26 (b) for all the post-stall model is interesting since, independently of the used post-stall model, there are no significant improvements in the predictions. It is clear that the analysed post-stall models fail to consistently improve the power coefficient prediction. 54

91 Globally, the model of Corrigan & Schillings (1994) perform better in bringing the predictions closer to the test data when compared with the other models. In general, the post-stall models have shown their ability to improve the performance prediction mostly in the thrust coefficient. The power coefficient is still significantly under predicted at low advance ratios. Further comparisons comprising forces distributions along the blade may help to better understand the lack of accuracy of these models and it will be the subject of future work. (a) (b) (c) Figure Comparison between data predicted by JBLADE using different post-stall models and data from NACA TR No. 594 (Theodorsen et al., 1937) for θ 75=30 (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 55

92 (a) (b) (c) Figure Comparison between data predicted by JBLADE using different post-stall models and data from NACA TR No. 594 (Theodorsen et al., 1937) for θ 75=45 (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 56

93 Inverse Design Methodology Validation In order to validate the inverse design methodology implementation in JBLADE (see Section 2.5.5), the light aircraft propeller presented by Adkins & Liebeck (1994) was designed through the Inverse Design sub-module, presented in Section Adkins and Liebeck Propeller The required data for propeller design are described in Table 3.1 and the resulting geometry is presented in Figure Table 3.1 Input data for propeller inverse design. Designation Units Power 52 kw Rotation Speed 2400 RPM Hub Diameter 0.30 m Tip Diameter 1.75 m Aircraft Velocity 49 m/s Lift Coefficient 0.7 No. of Blades 2 Observing Figure 3.27 is possible to conclude that JBLADE is in good agreement with original implementation done by Adkins & Liebeck (1994). (a) (b) Figure Validation of the inverse design methodology. (a) blade incidence angle (b) chord 57

94 The implementation was checked also against QMIL (Drela, 2005b) since it uses a different approach for introducing the airfoil characteristics. The results have shown that similar geometries are obtained for the given propeller operating point JBLADE vs Other BEM Codes In order to verify the reliability of JBLADE to accurately calculate the propellers performance, geometries presented in Section were simulated and the JBLADE predictions were compared with both experimental data and other existing BEM codes. The experimental data came from NACA TR 594 (Theodorsen et al., 1937) and NACA TR 530 (Gray, 1941) while the existing BEM codes selected to the comparison with JBLADE were the well-known QPROP (Drela, 2006) and JAVAPROP (Hepperle, 2010). NACA Technical Report 594 Observing Figure 3.28 (a), it is possible to conclude that JBLADE predicts a lower thrust coefficient in the smaller advance ratios region and closely match the experimental data in the higher advance ratio region. On the other hand, JAVAPROP (Hepperle, 2010) is correctly predicting the thrust coefficient for the smaller advance ratios and under predicting the thrust coefficient at bigger advance ratios region. The QPROP (Drela, 2006) is the code that performs worst for this situation, over estimating the thrust coefficient at smaller advance ratio and under predicting the thrust coefficient for the higher advance ratios. Regarding power coefficient (see Figure 3.28 (b)), it is possible to observe that JBLADE is correctly predicting the power coefficient over all advance ratios. JAVAPROP is correctly predicting the propeller s power coefficient for the advance ratios between 0.2 and 0.4. Out of this advance ratio range, JAVAPROP is significantly under predicting the power coefficient. QPROP is over estimating the power coefficient values in the smaller advance ratios region and under estimating the values for the bigger advance ratios. The propeller s efficiency results are shown in Figure 3.28 (c). Observing this figure, it is possible to conclude that both JAVAPROP and QPROP codes are correctly estimating the efficiency until an advance ratio about 0.5. However both codes estimate a smaller propeller efficiency at a smaller advance ratio. JBLADE, despite the fact that is slightly under estimating the efficiency (obtaining a maximum efficiency prediction close the other codes) is correctly predicting the advance ratio at which it occurs. 58

95 (a) (b) (c) Figure Results of NACA TR 594 (Theodorsen et al., 1937) for θ 75=15 (a) thrust coefficient (b) power coefficient (c) propeller efficiency. Figure 3.29 (a) presents the thrust coefficient predictions of the JBLADE, JAVAPROP and QPROP codes. It shows that JBLADE is correctly predicting the thrust coefficient over all advance ratios, matching the experimental data. JAVAPROP is under predicting the thrust coefficient over the advance ratios while QPROP code is over estimating the thrust coefficient at smaller advance ratios but correctly predicting the thrust coefficient values for the zero thrust condition of the propeller. Power coefficient results are shown in Figure 3.29 (b), showing that all the codes are significantly under estimating the power at low advance ratios. It was found that the cause may 59

96 be attributed to the airfoil s 360º angle of attack range airfoil polar misrepresentation just above the stall. Moreover, JBLADE and QPROP are slightly over estimating the power coefficient in the higher end while JAVAPROP is under predicting the power coefficient values. (a) (b) (c) Figure Results of NACA TR 594 (Theodorsen et al., 1937) for θ 75=30 (a) thrust coefficient (b) power coefficient (c) propeller efficiency. Figure 3.29 (c) shows that JAVAPROP is under predicting the propeller efficiency and the advance ratio at which maximum efficiency occurs. The QPROP code is slightly over predicting the efficiency in the advance ratios range between 0.2 and 0.6 and under estimating the maximum efficiency values. However QPROP, together with JBLADE, are correctly predicting 60

97 the advance ratio at which maximum efficiency will occur. The JBLADE software is also under estimating the maximum efficiency value. (a) (b) (c) Figure 3.30 Results of NACA TR 594 (Theodorsen et al., 1937) for θ 75=45 (a) thrust coefficient (b) power coefficient (c) propeller efficiency. Figure 3.30 (a) shows that JBLADE is correctly estimating the thrust coefficient. The JAVAPROP code is under estimating the thrust coefficient values in the smaller advance ratios region but correctly predicting the thrust for advance ratios bigger than 1.2. The QPROP code, despite the 61

98 over estimation of the thrust coefficient between 0.5 and 1.6 is also correctly predicting the thrust coefficient values for the bigger advance ratios. Figure 3.30 (b) shows that all the BEM codes are under predicting the power coefficient in the smaller advance ratios region. The JBLADE is correctly predicting the power coefficient for bigger advance ratios while JAVAPROP and QPROP are, respectively, under predicting and over estimating the power coefficient values. The propeller efficiency results (see Figure 3.30 (c)) shows that the propeller efficiency is over predicted in the advance ratios up to 1.5 by all the BEM codes. For bigger advance ratios JAVAPROP shows a slightly over estimation of the maximum efficiency value while JBLADE is estimating a maximum efficiency about 10% lower than the experiments. However, the advance ratio for the maximum efficiency closely matches the experimental values. This is related to the over prediction for power coefficients at high advance ratios. Comparing JBLADE with the JAVAPROP (Hepperle, 2010) and QPROP (Drela, 2006) codes, it was shown that JBLADE gives the best overall results. The ability to correctly predict the thrust coefficient over the advance ratios, while predicts the power coefficient as good as the other existing BEM codes, makes JBLADE the most accurate BEM code to obtain the propeller performance predictions. NACA Technical Report 530 Since the QPROP was the code that performed worst in the previously presented test cases, it was decided to compare the JBLADE predictions only with JAVAPROP estimations. The thrust coefficient results for the NACA TR No. 530 (Gray, 1941) propeller with θ 75 = 30 are presented in Figure 3.31 (a). It shows that both JBLADE and JAVAPROP are correctly predicting the thrust coefficient with JBLADE performing slightly better in the bigger advance ratios region. Figure 3.31 (b) confirms that the power coefficient obtained in JBLADE is under predicted at low advance ratios. However, contrary to what occurs in previous test case (see Figure 3.29 (b) and Figure 3.30 (b)), the power coefficient is much closely estimated in the higher advance ratios. JAVAPROP code presents even a bigger under estimation of the power coefficient at smaller advance ratios. Moreover, it also under predicts the power coefficient in the bigger advance ratios region. Propeller efficiency results (see Figure 3.31 (c)) shows that JAVAPROP is overestimating the propeller performance in the advance ratio range between 0.1 and 0.6. The maximum efficiency values prediction of both codes are coincident and slightly under estimating. The value of the advance ratio at which the maximum efficiency occurs is quite well estimated by both JBLADE and JAVAPROP. 62

99 (a) (b) (c) Figure 3.31 Results of NACA TR 530 (Gray, 1941) for θ 75=30 (a) thrust coefficient (b) power coefficient (c) propeller efficiency. The thrust coefficient (see Figure 3.32 (a)) is significantly over estimated by JBLADE for the advance ratios between 0.5 and 1.2. In addition, the thrust coefficient is slightly under predicted at bigger advance ratios but the JBLADE prediction is still closer to the experimental data than the JAVAPROP estimations obtained for this test case. 63

100 (a) (b) (c) Figure Results of NACA TR 530 (Gray, 1941) for θ 75=40 (a) thrust coefficient (b) power coefficient (c) propeller efficiency. Regarding power coefficient, presented in Figure 3.32 (b), it is observed that both JBLADE and JAVAPROP are under predicting the power coefficient in the smaller advance ratios region. However, the codes are giving better predictions in the bigger advance ratios region with a small advantage for the JBLADE software. Note that both experimental data and JBLADE prediction show a wave shape of the c t and c p curves at the lower end of the advance ratio. This behaviour is also observed in the experiments, although at a higher advance ratio. 64

101 Similarly to the previous test case, the advance ratio for the maximum propeller s efficiency (see Figure 3.32 (c)) the maximum efficiency is under estimated by both JBLADE and JAVAPROP codes. The maximum efficiency under prediction, in this test case, is related to the under prediction of the thrust coefficient at high advance ratios, since the power coefficient predicted closely match the experimental data for this advance ratio region. The codes under prediction of the power coefficient in the smaller advance ratios region lead to an over estimation of the propeller efficiency observed in the advance ratios between 0.2 and 1.1. (a) (b) (c) Figure Results of NACA TR 530 (Gray, 1941) for θ 75=50 (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 65

102 The thrust coefficient data obtained for the propeller with θ 75 = 50 (see Figure 3.33 (a)) show that JBLADE is slightly over estimating the thrust coefficient for the smaller advance ratios and under estimating it for the bigger values of the advance ratio. JAVAPROP is generally under predicting the thrust coefficient values over all the advance ratios, for this test case. Figure 3.33 (b) presents the results for the power coefficient and it possible to observe that both codes are under predicting the values of the power coefficient at small advance ratios. The predictions of both JBLADE and JAVAPROP for bigger advance ratios is close to the experimental data. The propeller efficiency data (see Figure 3.33 (c)) presents the same over estimation trend in the small advance ratios, due to the under prediction of the power coefficient in the smaller advance ratios. In addition, the maximum efficiency value is still under predicted by both JBLADE and JAVAPROP codes. The codes are also predicting a small advance ratio for the maximum efficiency value, when compared with experimental data. The JBLADE software confirms the best overall results for these NACA Technical Report No. 530 test cases. The advantage of the JBLADE in these test cases comes from the better predictions of the power coefficient, since it estimates always higher power coefficient values for small advance ratios, when compared with JAVAPROP. Adkins and Liebeck Propeller The propeller presented by Adkins and Liebeck was also computed with JBLADE and the performance predictions were compared with the data found on the literature. The blade geometry (see Figure 3.15 (a)) was replicated inside JBLADE and it was herein analysed in the off-design condition. The agreement between JBLADE and Adkins and Liebeck code as it is shown in Figure 3.34 is quite good. The differences between both codes in the low advance ratio region may come from the different approximations to the airfoil characteristics calculations done by different codes. However it was not possible to access the original code, and the results are compared only against the results published by Adkins & Liebeck (1994). The difference at Figure 3.34 (c) in the low advance region appears due to the different behaviour on the thrust coefficient results shown at Figure 3.34 (a). 66

103 (a) (b) (c) Figure Comparison between data predicted by JBLADE and data obtained from Adkins & Liebeck (1994). (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 67

104 APC 11 x4.7 Propeller (a) (b) (c) Figure Comparison between JBLADE predictions and data obtained from UIUC database for an APC 11 x4.7 for 3000 RPM (Brandt et al., 2014). (a) thrust coefficient (b) power coefficient (c) propeller efficiency. The comparison of the data predicted by JBLADE and experimental data obtained from UIUC Propeller Data Site (Brandt et al., 2014) for the APC 11 x4.7 propeller at 3000 RPM is presented in Figure Observing the thrust coefficient predictions (see Figure 3.35 (a)) it is possible to observe that JBLADE is in good agreement with experimental data for the smaller advance ratios region. However, for advance ratios bigger than 0.25 the JBLADE is predicting lower values of trust coefficient. Observing the Figure 3.35 (b) it is possible to observe the same behaviour, with JBLADE underpredicting the power coefficient for bigger advance ratios. 68

105 Since the advance ratio for the zero thrust condition as well as for the zero power condition are underpredicted, the advance ratio of the maximum efficiency is also underpredicted. (a) (b) (c) Figure Comparison between JBLADE predictions and data obtained from UIUC database for an APC 11 x4.7 for 6000 RPM (Brandt et al., 2014). (a) thrust coefficient (b) power coefficient (c) propeller efficiency. The data for the same propeller at 6000 RPM are presented at Figure 3.36 and also show that JBLADE is underpredicting both thrust coefficient (see Figure 3.36 (a)) and power coefficient (see Figure 3.36 (b)). Due to these underpredictions, the advance ratio for the maximum efficiency and the maximum efficiency (see Figure 3.36(c)) itself is underpredicted. 69

106 After a carefully analysis of the results and trying to understand what can be the origin of the difference between the simulations and the experimental data, the propeller performance coefficients obtained for different rotation speeds were found to grow when the rotational speed increases from 3000 RPM to 6000 RPM (see Figure 3.35 and Figure 3.36). This behaviour can be caused by the increase in the airfoil performance due to the Reynolds number increase. However, the XFOIL airfoil simulations did not show significant changes in the airfoil performance when the Reynolds number increases due to the increment in the rotation speed from 3000 RPM to 6000 RPM (see Figure 3.37). Figure Airfoil performance of the APC 11 x4.7 propeller obtained at r/r=0.75 for 3000 RPM and 6000 RPM. Other hypothesis was then formulated, based on the fact that propeller airfoil is very thin and the blades are susceptible to deform at higher rotational speed and thrust loadings, increasing its pitch angle. To verify this hypothesis, new simulations of the APC 11 x4.7 propeller were made in JBLADE considering a 1º and 2º increment on the blade s incidence angle. The results obtained with the new simulations seemed to be compatible with the hypothesis formulated, in which the blade was deformed to an increased pitch at 3000 RPM and even further at 6000 RPM, although more research needs to be done on this subject to measure the deformation. This blade deformation hypothesis lead to the implementation of a structural sub-module in the JBLADE in order to predict the deformation of the blades and allowing the user to perform an additional iteration loop to obtain the performance estimation of the deformed propeller. This Structural sub-module implementation and validation is described in detail in Section Structural Sub-Module Validation The formulation presented in Section 2.6 was implemented inside JBLADE as a new sub-module, described in Section In order to validate the implementation of the theory, the results obtained in JBLADE for different propellers blades (see Table 3.2) were compared with simulations performed in the structural sub-module of CATIA V5. 70

107 CATIA simulation validation In order to validate the structural analysis inside CATIA a new structural simulation was defined. The blade was divided into 20 sections in order to apply the distributed force obtained in JBLADE as a group of discrete forces along the blade. The blade material was properly defined and the normal force previously calculated in the Propeller Simulation sub-module was then exported and inserted in CATIA for each respective section. An example of the results produced by a CATIA analysis is presented at Figure The blade was considered as a cantilevered beam and the displacement of each section was exported in order to be compared with JBLADE data. Figure 3.38 Example of a bending Simulation in CATIA v5. A mesh independency study was performed using Blade 5 (see Table 3.2), since it uses different airfoils, and it is a tapered blade, with non-uniform chord along the span, representing the more complex test case. Three meshes were defined and as it is possible to observe in Figure 3.39, the difference in the maximum displacement between the Used Mesh and the Refined Mesh is about %. Thus, all the simulations in CATIA were performed with the intermediate mesh, saving some computational time. Figure 3.39 Mesh independency study performed in CATIA for Blade 5. 71

108 Blade s geometrical properties validation Concerning the blade s volume and mass calculations, five different blades were designed in JBLADE. The airfoils used (see Table 3.2) in the blades were exported from JBLADE and the blades were then built using the multi-section body tool in CATIA. Different structural concepts were used, as presented in Table 3.2: a completely solid blade (with different materials), a blade with a thin skin, and a blade with a skin and core material. Each blade was divided into 20 sections along which the properties were verified. Table 3.2 Blade Definition for Structural Sub-Module validation. Root Tip Structure Material Root Tip Span, Chord, Chord, Concept Airfoil Airfoil m m m Blade 1 S1223 S Solid Aluminium Blade 2 NACA 0012 NACA Solid Pine Wood Blade 3 NACA 0012 NACA mm skin thickness Aluminium Blade 4 NACA 0012 NACA mm skin + Aluminium Core Material + Rohacell Blade 5 NACA 4412 NACA Solid Aluminium The properties of the materials used in the blades are presented in Table 3.3. Table 3.3 Properties of the Materials used in the blades. Material Density, Young Modulus, Shear Modulus, kg/m 3 GPa GPa Aluminium Pine Wood Rohacell 110 A The results of volume and mass estimations obtained in JBLADE were compared with CATIA (see Table 3.4) and it is possible to conclude that the difference between both software is always less than 0.1%. As expected, the worst result was performed for the blade 5, since it has different airfoils in the root and tip and different chords as well. The validation of the moment of inertia calculation (see Section 2.6.2) was also performed and the results are presented in Table 3.5 for the used airfoils. 72

109 Table 3.4 Volume and Mass comparison using JBLADE and CATIA V5. JBLADE CATIA Error, % Volume, Mass, Volume, Mass dm 3 kg dm 3 kg Volume Mass Blade Blade Blade Blade Blade It is shown that the bigger difference between the JBLADE and CATIA occurs for the I xx of S1223 airfoil. This may be attributed to the higher camber of the airfoil and its thin trailing edge. For all the NACA airfoils, the estimations obtained in JBLADE are in good agreement with the CATIA data. Table 3.5 2D Airfoil properties comparison using JBLADE and CATIA. S1223 NACA 0012 NACA 2312 NACA 4412 JBLADE CATIA Error, % I xx, m e e I yy, m e e Xcentroid, mm Y centroid, mm Area, cm I xx, m e e I yy, m e e X centroid, mm Y centroid,mm 6.85e Area, cm I xx, m e e I yy, m e e X centroid, mm Y centroid, mm Area, cm I xx, m e e I yy, m e e X centroid, mm Y centroid, mm Area, cm The results for the intermediate sections of Blade 5 are presented in Table 3.6, since the airfoils in the middle of the blade are intermediate shapes between the root and tip airfoils. Table 3.6 shows that JBLADE is correctly predicting the intermediate sections properties. The bigger 73

110 difference between JBLADE data and CATIA data occurs for the I xx of section 18. However even in this section the difference is small, below the 3.5%. Table 3.6 2D properties comparison using JBLADE and CATIA for intermediate sections of Blade 5. JBLADE I xx, m 4 CATIA I xx, m 4 Error % JBLADE I yy, m 4 CATIA I yy, m 4 Error % JBLADE Area, mm 2 CATIA Area, mm 2 Error % E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E E

111 JBLADE bending validation The blades presented in the Table 3.2 were simulated and the results for each blade are presented and they will be discussed below. Figure 3.40 Comparison of Bending calculated in JBLADE and CATIA for Blade 1. Figure 3.40 presents the results for Blade 1 that uses the NACA 0012 airfoil from root to tip with a constant chord of 0.2m. The results show a good agreement between the vertical displacement predicted by JBLADE and CATIA. The difference between both curves may be due to the difference in the I xx calculation (see Table 3.5). Since JBLADE predicts a higher I xx for the blade s cross section, it results in a smaller bending of the blade, when compared with CATIA. Figure 3.41 Comparison of Bending calculated in JBLADE and CATIA for Blade 2. The Blade 2 is similar to the Blade 1 but it is made from Pine Wood instead of Aluminium. The results are presented in Figure 3.41, and it is shown that JBLADE prediction of the blade s bending perfectly matches the CATIA simulation results. Since this blade uses a different material, it also shows that the JBLADE can correctly estimate the blade bending regardless the material selected for the blades. 75

112 Figure 3.42 Comparison of Bending calculated in JBLADE and CATIA for Blade 3. Figure 3.42 presents the results of the Blade 3. These results show that JBLADE is predicting less vertical displacement, and the difference increases towards the blade s tip. In all the simulations above, the vertical displacement was measured in the nodes of the upper surface of the blades. Since the Blade 1 and Blade 2 are completely solid, it was assumed that no internal deformation of the cross section occurred. However, for the case of the Blade 3, since the blade is composed only by a thin skin of aluminium, the blade s cross section had suffered a small deformation (see Figure 3.43). Thus, the values of the displacement along the blade s leading edge were collected and also compared with JBLADE results in Figure It was concluded that the difference in the vertical displacement between JBLADE and CATIA decreases, since the deformation on the blade s leading edge is smaller. Figure 3.43 Illustration of the skin deformation calculated in CATIA. The Blade 4 test case considers a constant section blade with a skin made by Aluminium and a Foam Core. The blade has a constant chord from root to tip, being similar to the Blade 3 test case. Figure 3.44 shows that the vertical displacement estimated by JBLADE is in good agreement with CATIA data. This good agreement can be explained by the presence of the core material, which prevents the deformation of the blade s skin. At the same time these results 76

113 also confirm that the difference between JBLADE and CATIA in the Blade 3 results came from the skin deformation of the blade. Figure 3.44 Comparison of Bending calculated in JBLADE and CATIA for Blade 4. Concerning the Blade 5 test case (see Figure 3.45), the displacement estimated by JBLADE is also in a good agreement when compared with CATIA results. The small differences in the vertical displacement along the blade s span may arise from the fact that the blade was divided only in 20 stations. Since it has a more complex shape than the blades used in the previous tests cases may be necessary to increase the number of sections. In fact, there are small differences in the I xx along the sections, as it is possible to observe in Table 3.6, which also contributes to the difference presented in Figure Figure 3.45 Comparison of Bending calculated in JBLADE and CATIA for Blade 5. The bending test cases presented above showed that JBLADE can be used to predict the blade s bending due to its produced thrust. This can help the user to design a more efficient propeller accounting with possible deformations (and the consequent losses of performance by the blade s airfoils) and helping the user to estimate the weight of the propeller, which can be crucial for the vehicles like MAAT cruiser airship. 77

114 JBLADE twist deformation validation In order to validate the twist deformation calculation in JBLADE the formulation described in Section was implemented in JBLADE and the propellers presented in Table 3.2 were validated through the comparison of JBLADE results with CATIA simulations. Figure 3.46 Example of a Twist Deformation Simulation in CATIA V5. A blade s twist simulation was defined in CATIA with respective twisting moments applied at 25% of the blade s chord. The moments were obtained in the JBLADE Propeller Definition and Simulation sub-module (see Section 3.1.5) and were then introduced in CATIA, as in Figure The results were then exported from CATIA and compared with the JBLADE results. The vertical displacement of the trailing edge was used to address the blade s twist. Figure 3.47 Trailing Edge Displacement Comparison for Blade 1. Figure 3.47 presents the comparison of JBLADE calculations and CATIA simulations for the Blade 1 test case. The results show that JBLADE is under predicting the trailing edge displacement when compared with CATIA. The properties of the blades were estimated using the J s (see Eq. 2.91), which may help to explain the difference between JBLADE and CATIA. 78

115 Since the JBLADE is predicting a bigger I xx for the S1223 airfoil (see Table 3.5), it will result in a smaller twist deformation for the same load. Figure 3.48 Trailing Edge Displacement Comparison for Blade 2. In Figure 3.48 it is possible to observe a JBLADE s good prediction of the trailing edge displacement along the blade s span for the Blade 2 test case. The biggest discrepancy between JBLADE and CATIA occurs at the tip of the blade, where JBLADE is predicting the trailing edge displacement around 11% more than CATIA. Figure 3.49 Leading Edge Displacement Comparison for Blade 3. The results of the Blade 3 test case are presented in Figure It can be seen that the agreement is not good. This can be attributed to the fact that this blade is made only with a 6 mm skin of aluminium. Therefore, CATIA shows large deformations of the skin (see Figure 3.43) that are included in the structural behaviour of the blade. On the other hand the skin deformation is not accounted in JBLADE. Another factor for the discrepancy may be that in JBLADE the bending deformation is accounted solely due to the thrust distribution along the blade while in fact there is some bending of the 25% chord line due to the actual torsion occurring around the elastic axis instead of the 25% chord line. JBLADE can be improved in the future, regarding this matter. For now it is not considered important regarding the propeller performance because this depends mostly on the torsion deformation distribution. In this 79

116 specific test case, the leading edge displacement was used as the comparison between JBLADE and CATIA, since the deformation is smaller on this region. The maximum difference occurs at the blade s tip with JBLADE predicting about 35% less leading edge displacement, since it does not account for any cross section deformation. Figure 3.50 Trailing Edge Displacement Comparison for Blade 4. Figure 3.50 shows the trailing edge displacement comparison for Blade 4 test case. Similarly to what was presented at Section , the JBLADE s predictions closely match the values obtained in CATIA simulations, since the core material present in this blade does not allow the cross section deformation. The small differences presented in Figure 3.50 may be attributed to the difference in the I yy estimation, presented in Table 3.5 for the NACA 0012 airfoil. Figure 3.51 Trailing Edge Displacement Comparison for Blade 5. The results for the Blade 5 test case are presented in Figure Maximum difference for the trailing edge displacement occurs around 750 mm and the difference between JBLADE and CATIA is around 25%. JBLADE is correctly predicting the behaviour of the deformation, following the trend obtained in CATIA. The difference come from I xx along the span as well as from the twisting constant J s, since JBLADE uses only an approximation based in the cross section area, chord and section s I xx. 80

117 The test cases presented above have shown that JBLADE is capable to correctly predict the blade s deformation, helping the user to avoid possible damages on the designed propellers. In addition, looking to the absolute values of the twist validation test cases it is possible to conclude that the values are small and even differences of about 10% are almost unnoticeable and they will not affect the propellers s performance in a significant way. 81

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119 Chapter 4 Comparison between Computational Fluid Dynamics and XFOIL Predictions for High Lift Low Reynolds Number Airfoils Blade Element Momentum theory is an extensively used technique for calculation of propeller aerodynamics performance. To use this method the airfoil data need to be as accurate as possible in order to allow the correct calculation of the loads and power using the BEM code. At the same time, Computational Fluid Dynamics methods are becoming increasingly popular in the design and optimization of devices that depend on aerodynamics. For fixed and rotary wings applications, the airfoil lift over drag coefficient is what most determines the device s performance such that selecting a suitable computational tool is crucial for the design engineer. In the case of airfoils operating at low Reynolds numbers (60 000<Re< ), an accurate prediction of the transition position along the chord is essential to correctly simulate their performance characteristics. It has been shown (Selig, 2003) that XFOIL code has this capability and is widely used for airfoil design and optimization. However, it is unclear if recent transition and turbulence models can produce better airfoil performance predictions. The XFOIL Code, the Shear Stress Transport k-ω turbulence model and a refurbished version of k-kl-ω transition model were used to predict the airfoil aerodynamic performance. These airfoil performance predictions are compared to evaluate if CFD could improve JBLADE propeller performance estimation. 83

120 4.1 - Theoretical Formulation k-kl-ω model The work of Mayle & Schulz (1996), was responsible for setting the foundations for the laminar kinetic energy theory. The latter theory accounts for the kinetic energy of the velocity fluctuations that occur within the laminar boundary layer pre-transitional region. These velocity oscillations were measured for the first time in 1937 as a result of the pioneer experimental work of Dryden (1937). It was concluded that the free-stream turbulence was responsible for the occurrence of such boundary layer perturbations. Taylor (1939) made an interesting observation regarding these pre-transitional laminar velocity fluctuations. It was acknowledged that these oscillations were related with thickening and thinning of the boundary layer. Later in 1971, the experimental work of Klebanoff (1971) explicitly identified these stream wise fluctuations, naming them as breathing modes. However, Kendall (1991) renamed these velocity oscillations as Klebanoff modes in honour of the original discoverer. Based on this new transition theory, many novel RANS transition models have been developed since then. In 2004, the numerical work of Walters & Leylek (2004) presented a locally formulated laminar fluctuation kinetic energy transition model. The turbulence transition closure was named k kl ε, and it was implemented in the commercial software Ansys Fluent. Later in 2008, Walters & Cokljat (2008) presented an improved version of the original 2004 transition model, the k kl ω. Besides the change in the turbulence length scale variable from ε to ω some model constants and functions were also modified. The k-kl-ω transition model can be resumed down to three transport equations. One for the laminar fluctuations kinetic energy, another for the turbulent kinetic energy and the last one for the specific turbulent kinetic energy dissipation rate. The incompressible transport equations are disclosed in Eq. 4.1 to Eq. 4.3: kl t = P kl + R BP R NAT D L + x k t = P k + R BP + R NAT ωk D T + x ω t = C ω ω 1 k P k t,s + ( C ω R fw 1) ω k (R BP + R NAT ) C ω2 ω 2 +C ω3 f ω α t f W 2 k y 3 + x [(ν + α t ) ω ] σ ω x [ν kl ] 4.1 x [(ν + α t ) k ] 4.2 σ k x 4.3 The production terms in Eq. 4.1 and Eq. 4.2 are based on velocity strain rate defined in Eq. 4.4 and Eq. 4.5: P k = ν T,s S

121 P kl = ν T,l S One of the most interesting features of this transition model is the turbulence scale division. Introduced in the work of Walters & Leylek (2004), this was also applied in the 2008 k kl ω transition model version (Walters & Cokljat, 2008). This concept has been shown to be present in fully turbulent boundary layers by Moss & Oldfield (1996) and Thole & Bogard (1996). The concept divides the turbulence in large and small scales. The large scale is related to the laminar fluctuation kinetic energy production through the "splat mechanism", as suggested by Volino (1998) and mentioned by Bradshaw (1994). The small scale is related to regular turbulence. The model assumes that far from wall surfaces the small scale turbulent kinetic energy is equal to the free-stream turbulent kinetic energy. The definition of the limiting length scale is obtained from Eq. 4.6, where λ T is the length of the small scale turbulence defined in Eq. 4.7: λ eff = min (C λy, λ T ) 4.6 λ T = k ω 4.7 The small scale turbulent kinematic viscosity is calculated in Eq. 4.8, making use of a collection of damping functions, which attempt to simulate various mechanisms, such as the shearsheltering effect presented in Eq. 4.9, the turbulence intermittency (see Eq. 4.10) and the kinematic and viscous wall effect as presented in Eq and Eq respectively. The last damping function is based on effective turbulent Reynolds number (see Eq. 4.13) and in order to satisfy the realizability of C μ, it is calculated according to Eq In the work of Walters & Cokljat (2008) and Walters & Leylek (2004), C μ is a simplified version of its original form according to the work of Shih et al. (1994) and Shih et al. (1995). ν T,s = f v f INT C μ k T,s λ eff 4.8 f SS = e^ [ ( C 2 ssνω v ) ] 4.9 k k L f INT = min (, 1) 4.10 C INT k TOT f W = λ eff λ T 4.11 f v = 1.0 e Re T A v 4.12 Re T = f W 2 k νω C μ = A 0 + A s ( S ω )

122 The remaining k-kl-ω transition model description can be found in the work of Walters & Cokljat (2008). The described transition model was implemented in the open-source software OpenFoam (Greenshields, 2015). After a systematic analysis and testing of the transition model some modifications were proposed by Vizinho et al. (2013). Application of such modifications yielded improved results. One of the applied changes to the model was made to the turbulence intermittency damping function f INT (see Eq. 4.10). This alteration avoids the fact that the original model predicts zero turbulent viscosity in the free-stream. This is so since k L exists only near wall surfaces. Therefore the proposed term is then calculated as presented in Eq. 4.15: new k = min (, 1) C INT k TOT f INT 4.15 Another relevant change in relation to the original model is the definition of turbulence Reynolds number, Re T (see Eq. 4.13). The classical literature definition of turbulence Reynolds number as used by several turbulence models(chang et al., 1995; Craft et al., 1997; Lardeau et al., 2004) was applied also in the modified transition model. This will result in an improved asymptotic skin-friction coefficient behaviour along the fully turbulent region of the flow. The altered term is presented in Eq Re T new = k νω 4.16 The original model's turbulence specific dissipation rate destruction term is C ω2 ω 2. It was observed that the latter had an excessive effect near the wall. Also, in the work of Craft et al. (1996) the presented turbulence model has a set of equations resembling the presented turbulent kinetic energy, k, and the specific turbulent kinetic energy dissipation rate, ω, of the k-kl-ω transition model. In the present work, instead of ω, the transported quantity is the turbulent kinetic energy dissipation rate, ε. The function of interest is C ε2. This is multiplied by the term responsible for the destruction of the turbulent kinetic energy dissipation rate. Near the wall, its influence is reduced. The proposed hypothesis is then the imposition of a damping function, f W, (see Eq. 4.11), multiplied to the C ω2 ω 2 term. The resulting term is given in the third element on the right side of Eq Dω Dt = C ω ω1 k P k + ( C ωr 1) ω f W k (R BP + R NAT ) C ω2 ω 2 f W C ω3 f ω α T f W 2 k y 3 + x [(ν + α t ) ω ] σ ω x A more detailed description of the modified k kl ω turbulence transition model version is available in the work of Vizinho et al.(2013). 86

123 Shear Stress Transport k-ω model The Shear Stress Transport (SST) k-ω model (Menter, 1992, 1994) is a two-equation eddyviscosity model. This Menter s SST formulation was developed to effectively blend the robust and accurate formulation of the k-ω model in the near wall region with the k ε model behaviour as the model switches to the latter away from the wall. The authors decided to choose the SST k-ω model due to its accuracy for a wide class of flows in which low Reynolds numbers airfoils are inserted as suggested in the literature (Bardina et al., 1997). The SST k-ω model has a similar formulation to the Standard k-ω model. The transport equations are defined as presented in Eq and Eq. 4.19: (ρk) + (ρku t x i ) = i x k (Γ k ) + G k Y x k + S k 4.18 and (ρω) + (ρωu t x i ) = i x ω (Γ ω ) + G x ω Y ω + D ω + S ω 4.19 The G k represents the generation of turbulence kinetic energy due to the mean velocity gradients, calculated according to Eq. 4.20: G k = ρu i u u 4.20 j x i The effective diffusivities for the k ω model are given by Eq. 4.21: Γ k = μ + μ t σ k 4.21 Γ ω = μ + μ t σ ω 4.22 Where σ k and σ ω are the turbulent Prandtl numbers for k and ω respectively and they are calculated as in Eq and Eq. 4.24: 1 σ k = F 1 + (1 F 1) σ k,1 σ k,2 1 σ ω = F 1 + (1 F 1) σ ω,1 σ ω, The turbulent viscosity μ t in Eq is computed as follows: 87

124 μ t = ρk ω 1 max [ 1 α, SF 2 a 1 ω ] 4.25 where S represents the strain rate magnitude. Low Reynolds Correction The low Reynolds correction implemented in Ansys Fluent modifies the α coefficient (see Eq. 4.25). This coefficient damps the turbulent viscosity and it is given by Eq. where: α = α ( α 0 + Re t /Re k 1 + Re t /Re k ) Re t = ρk μω Re k = α 0 = β i β i = Note that in the high Reynolds number form of the k ω model α = α = XFOIL The XFOIL (Drela, 1989) code combines a potential flow panel method and an integral boundary layer formulation for the analysis of the flow around airfoils. The code was developed to rapidly predict the airfoil performance at low Reynolds numbers and its convergence is achieved through the iteration between the outer and inner flow solutions on the boundary-layer displacement thickness. Thus, the XFOIL code calculates the viscous pressure distribution and captures the influence of limited trailing-edge separation and laminar separation bubbles. The XFOIL uses an approximate e N envelope method to calculate transition. With this method the code tracks only the most amplified frequency at a given point on the airfoil downstream from the point of instability to obtain the amplitude of that disturbance. Transition is assumed when this integrated amplitude reaches an empirically determined value. The appropriate amplification factor, N, to use into XFOIL calculations was calculated by Eq. 4.31, which was presented by van Ingen (2008): N = ln (Tu) 4.31 Where Tu represents the absolute turbulent intensity. In the present work N was set to the default value of 9, which corresponds to a wing surface in an average windtunnel (Drela, 1989). 88

125 4.2 - Numerical Procedure Mesh Generation In order to simulate the airfoils and compare the different Computational Fluid Dynamics (CFD) models, it was used a completely structured O-type mesh with the outer boundaries placed 30 chords away from the airfoil. The airfoil was defined with 250 points (see Section 3.2.2) and special attention was given to the regions near the wall in order to ensure y+<1. The details of the final used mesh is shown in Figure Boundary Conditions To simulate the airfoil at the desired chord-based Reynolds number, corresponding to those of the available experimental results given by the literature (𝑅𝑒 = 2.0𝑥105 ) a density based solver was used. The far boundary was considered as a pressure farfield using the Mach number input to prescribe the flow speed. The desired angle of attack was obtained using the appropriate flow direction vector components. The airfoil top and bottom surfaces were defined as wall and the fluid inside the domain was defined as air with ρ =1.225 kg/m3 and μ =1.79x10-5 Pa.s. y x Figure Detail of the mesh around the airfoil used to obtain k-ω and k-kl-ω predictions. 89

126 These procedures give the advantage to simulate all angles of attack with only one mesh (Silva et al., 2002). To correctly compute the lift and drag coefficients, the decomposition of the flow direction vector was used, according the Eq and Eq L = L cos(α) D sin(α) 4.32 D = L sin(α) + D cos(α) 4.33 where L and D are lift and drag, respectively, and L and D represent the components of the aerodynamic forces based on the original system of coordinates of Ansys Fluent Results E387 Airfoil The E387 airfoil was designed during 1960s by Richard Eppler. Since it was specifically designed to use on model sailplanes this airfoil represented a significant improvement over the other airfoils available at that time. The airfoil performance predicted for Re = 2.0x10 5 by XFOIL, k- kl-ω transition model and SST k-ω turbulence model (with and without low Reynolds corrections) are compared to the University of Illinois Urbana-Campaign (UIUC) (Selig & Guglielmo, 1997) wind-tunnel measurements in Figure 4.2 (a) and (b). E387 (a) Figure Aerodynamic characteristics of the E 387 airfoil measured at Penn State UIUC wind tunnel (Sommers & Maughmer, 2003) compared with the numerical simulations results (b) The results presented in Figure 4.2 show that all the models are in good agreement with the experiments. The XFOIL and SST k-ω turbulence model with the Low Reynolds corrections (k-ω SST Low Re) are capable to accurately predict the corners of low drag region, although they 90

127 are predicting a slightly higher maximum lift coefficient. Regarding the SST k-ω without low Reynolds corrections, since it is unable to predict transition, it does not replicate the sharp corners, although the maximum lift coefficient is well predicted. The refurbished version of k-kl-ω transition model presents better agreement with the experimental data than SST k-ω turbulence model without low Reynolds corrections. For the lower corner of low drag region this model can correctly predict the values of both lift and drag coefficients. In the direction of the top corner of the low drag region as the lift coefficient increases k-kl-ω transition model predicts a slightly higher drag coefficient for a given lift coefficient, making the curve appear a bit to the right when compared with the measurements. (a) (b) Figure Comparison of E387 airfoil pressure distributions measurements (McGee et al., 1988) and results obtained with the CFD models and XFOIL, for Re = 2.0x10 5. (a) α=0º (b) α=4º Figure 4.3 (a) and (b) shows the pressure distribution for an angle of attack of 0 and 4 degrees, respectively. The results obtained from the above described numerical methods are compared with the measurements presented by McGee et al. (1988). At an AoA of 0º, XFOIL and SST k-ω turbulence model are in a perfect agreement with experiments, while the modified k-kl-ω transition model slightly under predicts the pressure coefficient in the upper surface of the 91

128 airfoil. At the angle of attack of 4º, the behaviour of different used methods remain the same, with a slightly under prediction in the k-kl-ω transition model until x/c=0.6 In Figure 4.4 (a) the transition position versus lift coefficient is plotted with airfoil s drag polar in order to observe the parallelism between the position of the transition and the laminar bucket limits. It is clear that the less steep part of the transition curves correspond to the limits of the laminar bucket of the drag polar as shown in Figure 4.4. In particular, one can note the lift coefficient of the transition ramps as the corners of the low drag bucket of the airfoil. The lower surface transition ramp at lift coefficient of about 0.3 as the lower corner and the upper surface transition ramp at lift coefficient of about 1.15 as the upper corner of the low drag bucket. (a) Figure (a) Transition position of the E387 airfoil upper and lower surfaces. (b) Drag polar of E387 for Re= 2.0x10 5. (b) The turbulence model SST k-ω with low Reynolds corrections and XFOIL give a close prediction but the later estimates the larger laminar flow extent at lower lift coefficients. The modified k-kl-ω transition model shows the same trend but only matches closely the other models around a lift coefficient of 1.18, overestimating the laminar flow extent at higher lift coefficients. The relation between transition position and the laminar bucket of the drag polar demonstrates the importance of a correct prediction of the transition position during the development of a new airfoil. 92

129 S1223 Airfoil S1223 (a) Figure 4.5 Comparison between UIUC measurements (Selig & Guglielmo, 1997) and results obtained by CFD models and XFOIL for S1223 airfoil for Re = 2.0x10 5. (a) C L vs C D (b) C L vs α. (b) The S1223 airfoil was designed by Selig & Guglielmo (1997) to achieve a Cl max greater than 2 at Re = 2.0x10 5. The S1223 airfoil has % thickness and camber of 8.67%. The UIUC experimental measurements (Selig & Guglielmo, 1997) showed a maximum lift coefficient of approximately 2.2 with moderate stall characteristics (see Figure 4.5 (b)). Figure 4.5 shows the predictions for the S1223 airfoil polar. Since the turbulence model SST k- ω without low Reynolds corrections performed worst for the E387 airfoil (see Figure 4.2) it was decided not to use this model in the simulations done for the S1223 airfoil. For SST k-ω turbulence model with low Reynolds corrections, the agreement is good until the angle of attack of approximately 10º. Contrary to the predictions presented for the E387 airfoil, the k- kl-ω transition model does not predict the lower corner of low drag region accurately. However, the agreement for higher angles of attack is even better than the XFOIL predictions. For XFOIL, the maximum lift coefficient is well predicted, although it occurs in a lower angle of attack as it is possible to observe at Figure 4.5 (b). At higher angles of attack XFOIL tends to underestimate the drag coefficient. 93

130 (a) (b) Figure Comparison of S1223 airfoil pressure distributions for Re = 2.0x10 5. (a) α=4º (b) α=8º Figure 4.6 (a) shows the pressure distribution at α = 4 and it is possible to observe that all the models are presenting a similar behaviour. 94

131 Chapter 5 Propeller Design and Optimization for Application on the MAAT Cruiser Airship In this chapter it will be presented the design and optimization of a propeller for application on the MAAT cruiser airship. The propeller s design process was initiated from with the inverse design method as described in Section This allowed the determination of the blade geometric characteristics for the pre-determined cruise operating point. Different propellers were optimized with the inverse design method according to the chosen blade airfoil and airfoil operating point. The best design strategy can thus be found. These different propellers were then used in a parametric/sensitivity analysis in order to judge their relative merit in the overall flight envelope High Altitude Propellers Design and optimization of a high altitude propeller can be a challenging problem due to the extremely low air density and low temperature. This, in turn, causes a major drop in the blade operating Reynolds number and increase in the Mach number compared with the sea level operation. Even so, propellers have been and continue to be a choice for many of high altitude aircrafts: Egrett (1987), Condor (1988), Pathfinder (1993), Perseus A (1993), Perseus B (1994), Strato 2C (1995), Theseus (1996), Centurion (1998) and Helios (1999). Although there is only little information about these high altitude propellers, a brief description is presented below (see Table 5.1) Egrett The Grob Egrett (Egrett II, 1990, 1991) is a high altitude reconnaissance platform developed for the German and U.S. Air Forces. The aircraft is a single engine propeller driven aircraft, 95

132 intended to fly at about m and powered by a Garrett turboprop engine. It has a 4 bladed propeller with 3.04 meters in diameter that generates about 2773 N of thrust Condor The Condor (Colozza, 1998) was a high altitude unmanned military demonstration aircraft used by U.S. army in high altitude (about m) reconnaissance missions. The propeller employed in the Condor aircraft was a 3 bladed variable pitch propeller with 4.90 meters in diameter, intended to provide 1129 N of thrust. However there is no experimental measurements of the propeller, since the Hartzell Company have never tested it due to the propeller s size and aircraft s proposed flight regime Pathfinder The Pathfinder (Colozza, 1998; Monk, 2010) aircraft was constructed by Aerovironment Inc. as a high altitude solar powered aircraft. It was able to fly at an altitude of m, powered by 6 electric motors for propulsion which drive 6 fixed pitch propellers with 2.01 meters in diameter. The Pathfinder propellers have a 50.8 twist from the root to the tip Perseus Perseus (Perseus B, 1999) is a remotely piloted aircraft developed under NASA s Environmental Research Aircraft and Sensor Technology (ERAST) project. In its B version includes a propeller with 2 blades and 4.4 meters in diameter. The propeller was designed to absorb 50 kw of power at cruise altitude and it was designed using the XROTOR (Drela & Youngren, 2003), a propeller code developed at Massachusetts Institute of Technology. The propeller blades weigh about 7 kg and an electric motor is used to change their pitch Strato 2C The Strato 2C (Schawe et al., 2002) is a high altitude aircraft designed to perform its missions at altitudes up to meters. It uses two variable pitch propellers with 5 blades and a diameter of 6 meters. The propellers work at 640 RPM during the cruiser and their pitch is controlled through a hydraulic actuator driven by the propeller gearbox. However, above m their performance is severely affected by the flow separation decreasing their efficiency up to 66% at m. One of the causes identified for the observed decrease in the propellers efficiency may be the usage of not sufficiently carefully designed airfoils for the high Mach low Reynolds numbers conditions. 96

133 Theseus The Theseus (Merlin, 2013) was built by Aurora Flight Sciences, funded by NASA through the Mission To Planet Earth environmental observation program. It was a twin-engine, unpiloted vehicle, powered by two kw turbocharged piston engines that drove two propellers with 2.74 m in diameter. Propellers were designed to generate 409 N of thrust each one. Table 5.1- High-altitude propeller data. Year Aircraft Name Propeller Thrust, N Propeller Diameter, m T/A, N/m 2 Altitude, m 1987 Egrett (Egrett II, 1990, Egrett II, 1991) Condor (Colozza, 1998) Pathfinder (Colozza, 1998; Monk, 2010) Perseus (Perseus B, 1999) Strato 2C (Schawe et al., 2002) Theseus (Merlin, 2013) MAAT Cruiser Requirements To design a new propeller for application on the MAAT cruiser airship it was necessary to identify the airship s power requirements. Thus, the total thrust needed for the MAAT airship, provided by the MAAT consortium partners in charge with the cruiser aerodynamics, is presented at Table 5.2. The propeller s disk loading was initially selected based on the analysis of Table 5.1. After selecting the disk loading an initial study on the number of propellers needed to reach the total thrust was performed. Table 5.2- Initial Considerations for the study of number of propellers. Designation Units Total thrust N Disk loading 300 N/m 2 Total area of actuator disk m 2 The implemented parametric study (see Figure 5.1) shows that if 50 propellers are selected, each one needs to provide 6.8 kn of thrust. After some iteration on the inverse design method, it was decided to increase the maximum diameter from 5.3 m to 6 m, reducing the disk loading to around 240 N/m 2. The rotation rate was calculated using a fixed Mach number of 0.6 at the 97

134 blade s tip that resulted in 550 RPM. The airship s propulsive properties are presented in Table 5.3. Figure 5.1 Parametric study of the thrust for each propeller and their respective diameter. Table 5.3- MAAT cruiser propulsive system properties. Designation Units No. of Propellers 50 Thrust 6.79x10 3 N Rotation Speed 550 RPM Propeller Diameter 6 m Disk Loading N/m Propeller Design and Optimization The main goal of any propeller is to transfer the shaft power provided by the engine to the air stream as efficiently as possible. Propellers operating at high altitudes experience a number of unique design issues such as the aforementioned changes in the atmospheric conditions that must be addressed. These changes of atmospheric conditions with altitude are herein assumed to correspond to the International Standard Atmosphere (ISA) ( U.S. Standard Atmosphere, 1976). The main properties of the atmosphere at 16km altitude, in which the propeller will operate, according to ISA model, are summarized in Table 5.4. Table 5.4- Atmosphere Conditions for an altitude of 16 km. Designation Units Air Density kg/m 3 Absolute Viscosity 1.44x10-5 kg/(m.s) Speed of Sound m/s 98

135 Airfoil Development Since the blade airfoils L/D ratios are required as inputs into the inverse design methodology, different airfoils were analysed with the XFOIL module (see Figure 5.2) at the operating Reynolds and Mach numbers enabling an initial look at the airfoil characteristics. The L/D ratio has a small but noticeable effect on the final blade needed chord and twist. These ratios also have a significant effect on the propeller performance. (a) Figure Airfoils comparison performed in JBLADE s XFOIL sub-module for Re=5.00x10 5 and M=0.1 (a) C L vs C D (b) C L 3/2 /C D vs C L (b) The airfoil with highest L 3/2 /D from those that were initially considered, the NACA 63A514, was then set as a base airfoil and improved (Gamboa & Silvestre, 2013) in order to increase its L/D within a useful angle of attack range to reduce the power required by the propeller for the previously selected disk loading and thrust. Since the propeller was designed to operate at high altitudes, the blade chord calculated through the inverse design methodology tends to be big leading to propellers with high solidity. Figure 5.3 -Base and final airfoils shapes comparison and their pressure coefficient distribution for Re=5.70x10 5 and α=6.0º 99

136 The comparison between the base and the improved airfoils shape and pressure coefficient distribution along the chord is presented in Figure 5.3. Their polars are presented in Figure 5.4 and it is possible to observe that the improved airfoil presents higher L 3/2 /D and L/D ratios. (a) (b) (c) Figure Comparison between NACA 63A514 and improved airfoil for Re= 5.70x10 5. (a) C L vs α (b) C L vs C D (c) L/D vs C L (d) L 3/2 /D vs C L. (d) These maxima ratios occur for higher lift coefficients, leading to a reduction of the blade chord needed to generate a given thrust. The final airfoil polars were obtained for the relevant Blade and Mach number range in the JBLADE XFOIL module. These airfoil polars were then extrapolated such that the lift and drag coefficients became available for 360º airfoil angle of attack range (Morgado et al., 2013) A New High Altitude Propeller Geometry Design Concept The propeller design point consists on the airship s velocity, the thrust that the propeller needs to produce, the propeller hub and tip radius, the position of each intermediate section and the air density at the desired altitude. The Reynolds number at r/r=0.75 was then estimated for the selected operating point and used to calculate the airfoil aerodynamic characteristics. After 100

137 the extrapolation, the airfoil data were used in the Inverse Design sub-module, allowing the calculation of an initial blade geometry. High altitude propellers tend to have a high solidity factor due to the limitation in the blade tip speed for a given tip Mach number and the high altitude very low air density that limit the dynamic pressure acting on the blades. This problem leads to propellers with a high number of low aspect ratio blades. As an alternative to the traditional way of designing a propeller, in which the lift coefficient is prescribed along the blades span, JBLADE Software allows the usage of the airfoil s best L 3/2 /D or L/D. The use of the airfoil best L 3/2 /D as a blade design concept leads to a minimization of the needed chord along the blade, since the airfoil is operating at a higher lift coefficient than the typically used best airfoil L/D condition. To maximize the airfoils efficiency they can be individually optimized for the Reynolds number at their respective radial position, allowing even further blade chord reduction, maximizing the propeller s efficiency. According to some cases presented in the literature (Colozza, 1998; Koch, 1998) the same airfoil was used along all blade span. (a) (b) (c) Figure (a) Comparison of propellers geometries (b) L 3/2 /D Propeller (c) L/D Propeller After obtaining the initial geometry, the propeller performance was computed and the Reynolds and Mach numbers distributions along the blade radius (see Figure 5.6) were determined. The airfoil polars along the blade were updated for the actual distributions and the inverse design methodology was applied again. This procedure was repeated until no modifications were observed in the blade s chord and twist. 101

138 Figure Final Reynolds and Mach numbers distribution along blade radius for V = 28m/s at r/r=0.75 Two different propellers (see Figure 5.5) were produced following the above mentioned design methodology: one using the airfoil best L/D and the other with airfoil s best L 3/2 /D. For both designs, the hub radius was fixed at 0.2 meters and the tip radius was set to 3 m, according to the conditions defined in Table 5.3. The improved airfoil, presented in Section 5.3.1, was used along all the blades sections for both propellers. The results obtained for both propellers were compared with conventional CFD results obtained for the same geometries and they are presented in Section One of the objectives of this study was also to understand which concept (the L 3/2 /D or L/D) along the blade span will produce more efficient propellers. 102

139 Chapter 6 3D Propeller CFD Simulations In this chapter the Computational Fluid Dynamics simulations, performed for different propellers, will be presented. An APC 10 x7 SF propeller was simulated and the results were used to validate the new 3D Flow Equilibrium model, presented in Section The two propellers designed for application in the MAAT cruiser airship, presented in Section 5.4, were also simulated along their operational envelope. The propellers performance was then compared with JBLADE Software results, since there is no experimental data for these particular propellers geometries APC 10 x7 SF Propeller An APC 10 x7 SF propeller was used to validate JBLADE for low Reynolds number predictions. The airfoil of the APC 10 x7 SF propeller was obtained by Carvalho (2013) and introduced in JBLADE. The airfoil was then simulated for the proper Reynolds and Mach numbers distributions along the blade and the propeller was replicated using the geometry presented in Figure 6.1 in JBLADE and the propeller performance was computed for comparison with the CFD results. 103

140 (a) (b) Figure APC 10 x7 SF propeller geometry (Brandt et al., 2014) and its shape after introduced in JBLADE CFD procedure A CFD simulation of the propeller was performed in order to validate the new 3D Equilibrium formulation, presented in Section A commercial package of Ansys Fluent (ANSYS FLUENT Theory Guide, 2010) with the SST k-ω turbulence model (Menter, 1994; Menter et al., 2003) was used. The hybrid mesh (see Figure 6.2 and Figure 6.3) contains 2.89 million points and it was chosen to use an implicit integration of the incompressible Reynolds Averaged Navier- Stokes equations coupled with turbulent transport equations. Furthermore, the SIMPLE algorithm was used for pressure-velocity coupling. In order to consider the rotation of the propeller a Multiple Reference Frame (MRF) approach was adopted. Thus, the computational domain is divided in two regions: the internal domain which covers the propeller and it was rotating at 3000 RPM and the external domain which was considered to be stationary. Figure 6.2 Domain dimensions used to simulate the APC 10 x7 SF propeller. 104

141 The second order upwind scheme was used for the convection terms while the diffusion terms were discretized using the central scheme. The convergence of the numerical solution was controlled by assigning suitable under relaxation of the transport equations and observed that the relative numerical error of the solution dropped below The blade surfaces of the used mesh (see Figure 6.4) were defined by 300 nodes in the span wise and 100 nodes in the chord direction. Figure 6.3 Domain and boundary conditions used to simulate the APC 10 x7 SF propeller. Mesh independency tests were accomplished to ensure that the obtained results were not dependent of the selected mesh. As presented in Figure 6.5, three different meshes were used to ensure the independency of the results. The coarse mesh (see Table 6.1) was composed by 1.72 million cells, the used mesh was prepared with 2.89 million and the refined mesh consisted in 6.45 million cells. Figure 6.4- Distribution of the cells on the blade surface. 105

142 The mesh independence study was performed for an operating condition of 3000 RPM and a freestream speed of 5 m/s, corresponding to an advance ratio of about The air density was kg/m 3 and the air dynamic viscosity was set to 1.78x10-5 Pa.s. Regarding the thrust coefficient, the difference between the used mesh and the refined mesh was 0.92% while the power coefficient presented a difference of 0.24%. Concerning the propeller efficiency, the difference between refined mesh and used mesh was about 0.32%. Thus, since the result is not affected and in order to save time, the mesh with 2.89 million was used in the remaining calculations. (a) (b) (c) Figure 6.5 CFD Simulations mesh independency tests performed for APC 10 x7 SF propeller for 3000 RPM and 5 m/s. (a) thrust coefficient (b) power coefficient, (c) propeller efficiency. 106

143 Table 6.1- Number of cells of different meshes used in the mesh independency tests. Designation No. of Cells Coarse Mesh 1.72x10 6 Used Mesh 2.89x10 6 Refined Mesh 6.45x D Flow equilibrium validation The tangential velocity along an APC 10 x7 Slow Flyer radius was plotted together with CFD data and original BEM formulation in order to validate the new proposed model for 3D flow equilibrium (see Section 2.4.1). Figure Tangential velocity distribution along an APC 10x7 SF propeller (Brandt et al., 2014) blade radius, at 1 m behind the propeller plane, for CFD, original BEM formulation and new proposed 3D Flow Equilibrium model. It is seen in Figure 6.6 that the 3D Equilibrium hypothesis is a fair approximation with reality considering that the CFD results show the real trend. It is also clear the weakness of BEM in respect to the tangential induction since each annular element of the disk has no relation to its neighbour elements allowing discontinuities in the tangential induction profile. The under prediction of tangential velocity in the BEM simulation is related to the lower power coefficient that results from its formulation in this static thrust condition. The simulations were performed for static condition at 3000 RPM. The air was defined with a density of kg/m 3 and a dynamic viscosity of 1.78x10-5 Pa.s Performance prediction Figure 6.7 shows that both JBLADE and CFD simulations predictions follow the experimentally measured thrust coefficient. In the lower advance ratios region, the JBLADE predicted thrust coefficient values are over predicted while the CFD thrust coefficient is slightly over predicted, 107

144 compared with the experimental measurements along all advance ratios. Considering the whole advance ratio interval, JBLADE predictions are closer to UIUC experimental data for the thrust coefficient than the CFD results. Regarding the power coefficient calculations, JBLADE and CFD simulations agree with the measurements. The difference between JBLADE and UIUC experiments increases moderately with the increase in the advance ratio. The difference between CFD simulations and experimental values is constant, with a slight over prediction from CFD calculations. (a) (b) (c) Figure 6.7 Performance prediction comparison for APC 10 x7 SF propeller (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 108

145 The JBLADE prediction is higher at low advance ratios and drops to under predicted values for high advance ratios. Nevertheless, the difference in JBLADE to the experimental data remains smaller than that of the CFD results. JBLADE and CFD simulations correctly predict the maximum efficiency of the propeller as well as the advance ratio value for its maximum. However, while JBLADE predicts the zero efficiency limit at an advance ratio lower than the experiments, CFD predicts that zero efficiency for a higher advance ratio. Overall the JBLADE predictions are closer to the experimental data than the CFD results for the low Reynolds APC 10 x7 SF propeller. Figure 6.8 shows the distribution of the pressure on the blades surfaces and iso-surfaces of the velocity magnitude in the flow field. Figure Pressure distribution on blade surface and velocity magnitude distribution on the isosurfaces for V =1 m/s and 3000 RPM MAAT Cruiser Propeller CFD procedure The computational fluid dynamics simulations were performed for the possibility to study the features of the flow structure and to obtain more detailed information, in order to identify the parameters that affect the flow and the efficiency of the propeller. Since there is no experimental data for the designed cruiser propeller, the numerical simulations were done and used to compare with JBLADE software results. Figure Example of the blade geometry transformed into a CAD part for meshing purposes. 109

146 The airfoils used in the CFD simulation were exported from JBLADE and imported into the CATIA V5 CAD software. Each section was translated making the xx axis coincident with the 25% of the chord. The airfoils were then rotated according to Figure 5.5 (a) and a multi-section body was generated (see Figure 6.9). The mesh was generated and the computational domain was composed of about 2 million of tetrahedral cells clustered around the blade surface as it is presented in Figure The boundaries of the domain representing the free stream conditions were set at 3 radius to the inlet and 10 radius to the outlet. Figure Representation of the computational domain and its boundary conditions The blade surfaces walls (see Figure 6.11) were defined by 300 nodes in the span wise and 200 nodes on the chord direction. Figure Distribution of the cells on the blade surface. Mesh independency tests were performed to an operating condition of 550 RPM and a freestream speed of 30 m/s, corresponding to an advance ratio of about The air density was kg/m 3 and the air dynamic viscosity was set to 1.44x10-5 Pa.s ensure that the obtained results are not dependent of the used mesh. As presented in Figure 6.12, three different grids 110

147 were used to ensure the results mesh independency. The coarse mesh (see Table 6.2) was composed by 1.65 million cells, the used mesh had 2.7 million and the refined mesh consisted in 4.18 million cells. The maximum discrepancy between the used mesh and the refined mesh was 3.9% for thrust coefficient and 4.2% for the power coefficient. Thus, since the results were not significantly affected by the mesh and in order to save computational time the mesh with 2.7 million cells was used in the remaining calculations. Table 6.2- Number of cells of different meshes used in the mesh independency tests. Designation No. of Cells Coarse Mesh 1.65x10 6 Used Mesh 2.7x10 6 Refined Mesh 4.18x10 6 Furthermore, in order to reduce the computation time and facilitate the meshing process, periodic boundary conditions were used. The y + was controlled by the external refinement of the mesh near the blade, through the creation of prismatic cells around the surface of the blade such that the first point above the blade surface had a value y + <1. As presented in Figure 6.10, the inlet, the outlet and the far domain were stated as a pressure far field boundaries. At the inlet the flow speed and direction is prescribed by inputting the value of the Mach number and the direction of the flow along the domain, together with the values of static pressure and temperature. The value of turbulent intensity and viscosity assigned to these boundaries were 0.1 % and 10 respectively. The value of the pressure and temperature were changed according to ISA models to correspond to an altitude of meters above sea level. The blade surface was defined as wall with no slip because the blade was considered stationary wall in respect to the adjacent rotating zone. Numerical simulations of steady compressible Reynolds-Averaged Navier-Stokes (RANS) equations and the turbulent mode with absolute velocity formulation were accomplished by discretizing each governing equation within the Finite Volume Method (FVM) using a cell centred collocated arrangement of primitive variables. Moreover, the k-ω SST turbulence model (Menter, 1994) was used to deal with the time-averaging of the closure equations and for simulating the turbulence. 111

148 (a) (b) (c) Figure Mesh independency study made for L 3/2 /D propeller at V=30 m/s. (a) thrust coefficient (b) power coefficient, (c) propeller efficiency. The domain was divided in two regions: the rotating and stationary zones as presented in Figure The Multiple Reference Frame (MRF) method was chosen to consider the blade rotation, preventing the need to perform transient calculations by solving the governing equations in a rotational reference frame, by considering the centripetal and Coriolis acceleration. This method is more suitable for steady state simulations where the unsteadiness of the problem can be ignored. Also the implicit coupled density based solver available in Ansys Fluent was selected for the coupling of the momentum and continuity equations. Spatial discretization of the flow convective fluxes and turbulence variables were performed by the higher order advection upstream splitting method (AUSM) schemes and second order upwind scheme respectively. Moreover, least square cell based method was used for all gradients. 112

149 The rotational speed of 550 RPM was considered for the rotating domain. For improving the convergence of the solution, the rotational speed was increased gradually from 100 RPM to the final rotational speed of 550 RPM. The convergence of the numerical solution was controlled by assigning 1 to the courant number for the iterative solution and considering suitable under relaxation factors for the turbulent variables. The convergence of the solution was also guaranteed by monitoring the relative numerical error of the solution to drop below In order to compare the results of the numerical simulation with the obtained results from the JBLADE software, the propellers were tested over a range of free stream velocity between 10 m/s and 65 m/s Performance prediction (a) (b) (c) Figure Comparison between data predicted by JBLADE and CFD for the designed propellers: (a) thrust coefficient (b) power coefficient, (c) propeller efficiency. 113

150 Contrary to the methods used in which the airfoil lift coefficient is prescribed along the blade span, in these designed propellers, the airfoil s best L 3/2 /D and the airfoils best L/D were used to obtain 2 different propellers (see Section 5.4). The performance of the propellers is presented in Figure Observing Figure 6.13 it is possible to observe that JBLADE predicts a bigger thrust coefficient than CFD in the lower advance ratio region. This over estimation drops as the advance ratio increases. At the higher advance ratios, JBLADE and the CFD data tend to agree. The results also show that the power coefficient is also over estimated by JBLADE at low advance ratios when compared with the CFD simulations. Due to the differences presented in thrust and power coefficient, the propeller efficiency is over predicted by JBLADE when compared with the CFD results. The advance ratio for the maximum efficiency is 1.05 for JBLADE against 0.9 obtained with CFD but the maximum efficiency is estimated to be 10% higher than the CFD simulations values. This is related to the JBLADE s over prediction of the thrust coefficient at high advance ratios. More than comparing JBLADE results with the CFD simulations, Figure 6.13 also shows that JBLADE correctly predicts the difference between the two different design concepts. Notably, the proposed new concept of optimizing the operating L 3/2 /D of the blade's airfoil results in a more efficient propeller. The difference also appeared in CFD simulations and it is possible to conclude that JBLADE can be successfully used to produce different propeller geometries and select the relative best one to proceed to the next design phase. In order to further understand the merit of designing the blade for optima L 3/2 /D on the performance, the distribution of the skin friction on the two distinct blades are compared in Figure 6.14 and Figure 6.15 for the same operating point with a freestream speed of 50 m/s, and at 550 RPM, corresponding to an advance ratio of about (a) Figure Skin friction coefficient distribution on upper surface for an advance ratio of (a) L 3/2 /D Propeller (b) L/D Propeller. (b) 114

151 Figure 6.14 and Figure 6.15 clearly show that the skin friction coefficient of the blade designed using concept of maximizing L/D is higher than the skin friction coefficient on the blade designed using the airfoil s best L 3/2 /D. This is not beneficial for the performance of the blade, since the input power will be partly used to overcome the extra drag caused by the blade shape. Most of these losses are occurring near the leading edge of the airfoil and mostly in the tip region of the blade. This clearly relates to the higher efficiency of the best L 3/2 /D blade propeller seen in Figure (a) (b) Figure Skin friction coefficient distribution on lower surface for an advance ratio of (a) L 3/2 /D Propeller (b) L/D Propeller. Another parameter that could be used for analysing the blade design is the pressure coefficient (see Figure 6.16 and Figure 6.17). The main component of the thrust is originating from pressures forces. The blade s thrust generation capability increases with the increase in the difference of the pressure between upper and lower sides of the propeller s blade. (a) (b) Figure Pressure distribution on upper surface for an advance ratio of 0.91 (a) L 3/2 /D Propeller (b) L/D Propeller. 115

152 When the blade is rotating, the lower pressure appears on blade s upper side and the higher pressure appears on the blade lower side. The biggest difference of pressure distributions appears on the blade s tip while at blade root the difference is smaller. (a) (b) Figure Pressure distribution on upper surface for an advance ratio of (a) L 3/2 /D Propeller (b) L/D Propeller. The comparison of the two distinct design concept blades reveals that the propeller designed with maximum L 3/2 /D concept provides higher pressure differences all over the blade surface, which means that the propeller produces higher thrust when compared with the propeller designed with airfoil s best L/D concept. 116

153 Chapter 7 Wind Tunnel Low Reynolds Propeller Testing This chapter presents the development of the experimental setup for low Reynolds propeller testing. The data obtained with the developed experimental setup were compared against reference experimental data to validate the installation Experimental Setup Wind tunnel The tests were performed in the subsonic wind tunnel of the Aerospace Sciences Department at University of Beira Interior, presented in Figure 7.1. Figure 7.1 Wind tunnel of Aerospace Sciences Department. 117

154 The wind tunnel is an open-return type with a 6.25:1 contraction ratio. The test section is nominally 0.8 m x 0.8 m in cross section, with 1.5 m length. The maximum speed available at the test section is about 33 m/s, obtained through a 15 kw alternated current motor, connected to a six-bladed fan. In addition, the wind-tunnel settling chamber contains a honeycomb and two anti-turbulence screens allowing a good flow quality in the test section Thrust Balance Concept In order to measure the performance of the propellers it was necessary to develop a new test rig. The design selected for the thrust balance, shown in Figure 7.2, is similar to the T-shaped pendulum structure originally built in UIUC (Brandt & Selig, 2011). An effort was made to reduce the complexity of the assembly inside the wind tunnel test section, in order to ensure minimal flow and measurements disturbances. The position of the load cell can be modified according to the propeller s expected thrust, in order to use the full scale of the load cell for different propellers, reducing the measurements errors and uncertainties. Flexural pivots were chosen over the standard bearings since they greatly reduce the adverse tendencies that affect the standard bearings, when used in static applications, namely friction and stiction. Figure 7.2 Thrust Balance Concept (Alves, 2014). The pendulum was designed in order that the propeller, and consequently the thrust vector, were located at the centre of the test section. Additionally, a preload weight, as presented in Figure 7.2, was added to the balance, maintaining the load cell in tension throughout the complete advance ratio range. This pre-load weight ensures that the load cell does not reach the negative thrust conditions. The detailed development of the thrust balance can be found at Alves (2014). 118

155 Thrust and Torque Measurements A FN3148 Load Cell (2012) (see Figure 7.3 (a)), manufactured by FGP Sensors & Instrumentation, was used to measure the propellers thrust. This load cell has a maximum capacity of 100 N for both tension and compression. Regarding the torque measurements, it was used a reaction torque sensor, model RTS-100 (see Figure 7.3 (b)), produced by Transducer Techniques (RTS- 100, 2014). Both sensors are connected to a shielded connector block (SCB-68, 2009), produced by National Instruments. Thrust Load Cell (FN 3148) Reaction Torque Sensor (RTS-100) (a) (b) Full Scale: 100N Rated Output 1.5mv/V nominal Tension and Compression Capacity: 100 in-oz Accuracy: 0.05% of Full Scale Clock Wise/Counter Clock Wise Integrated Mechanical Stops Non Repetability : 0.05% of Rated High Level Outup Model Output with Integrated Amplifier Shielded Connector Block (SCB-68) (c) Shielded I/O connector block for use with 68-pin X, M, E, B, S, and R Series DAQ devices Screw terminals for easy I/O connections or for use with the CA general-purpose breadboard areas Figure 7.3 Sensors specifications (a) Thrust load cell (b) Torque Reaction Sensor (c) Shielded Connector Block. 119

156 Propeller rotation speed measurement A Fairchild Semiconductor QDR 1114 (2013) photo reflective object sensor was used to measure the propeller rotational speed. This sensor is used to count the number of revolutions that the shaft makes in a fixed time interval, resulting on an accuracy of ±0.5 Rev/0.75 s. The sensor circuit, comprising an infrared emitting diode, a phototransistor and a photo reflector circuit (see Figure 7.4), was developed by Santos, (2012) to make the output signal independent of the distance from the reflecting surface. With this circuit the sensor can be placed up to 2 mm from the reflective surface. The output voltage switches between 0.27 V when the sensor is pointed to a white surface and 4.61 V when the sensor is pointed to a black surface. The circuit has a response time of around 50 μsec. Since the rotational speed of the tested propeller had never exceeded 7000 RPM, the output voltages and response time of the circuit proved to be sufficient for accurate rotation speed measurements. Figure Photoreflector circuit s schematics (Santos, 2012) Free stream flow speed measurement The freestream velocity is measured with a differential pressure transducer, an absolute pressure transducer and a thermocouple. The measuring mechanism uses two static pressure ports, one at the tunnel settling chamber and another at the entrance of the test section as presented in Figure 7.5. Figure 7.5 Wind tunnel Schematics with representation of the static pressure ports location. 120

157 The contraction section causes an increase in velocity and consequently, a decrease in the pressure at the test section. The pressure difference between the wind tunnel settling chamber and the test section is a measure of the flow rate through the tunnel. Thus, the velocity can be determined through Bernoulli s equation: p 1 ρ V gz 1 = p 2 ρ V gz Considering that the tunnel is horizontal, z 1 = z 2, then: V 2 2 V 1 2 = 2(p 1 p 2 ) ρ 7.2 Relating the velocities from the 1D incompressible continuity relation: A 1 V 1 = A 2 V or V 2 = A 1 A 2 V Combining Eq. 7.12, Eq. 7.3 and Eq. 7.4, the flow velocity in the test section is calculated by: V 2 = 2(p 1 p 2 ) ρ [1 ( A 2 A 1 ) 2 ] 7.5 The atmospheric pressure outside of the tunnel is measured with an absolute pressure transducer made by Freescale Semiconductor model MPXA4115A (2009). The temperature is measured with a National Instruments LM335 (1999) thermocouple located at the inlet of the wind tunnel Balance Calibration Before using the rig for any tests, each measuring instrument was calibrated. For the torque sensor calibration (see Figure 7.6 (a)), calibrated weights were used with a known length to create a calibration torque, and by adding and removing weights, a linear relationship between the torque and voltage was calculated. Regarding the thrust calibration, it was made in situ using calibrated weights and a low-friction pulley system to create an axial load simulating the propeller thrust on the load cell (see Figure 7.6 (b)). By increasing and decreasing a known force on the load cell, a linear relationship between the thrust and voltage was determined. These calibration procedures need to be regularly performed to ensure consistent results. 121

158 Calibration was later verified using check-loads. Pure and combined check-loads were repeatedly applied to verify the balance calibration. (a) Figure 7.6 Illustration of calibrations procedure (Alves, 2014). (a) Torque sensor (b) Thrust load cell. (b) Test Methodology To perform the static performance tests, the propeller thrust and torque were measured along with the local atmospheric pressure and temperature at different RPM. Regarding the dynamic performance tests, with freestream speed, the propeller rotational speed was set to the desired value and the wind tunnel's freestream velocity was increased from 4 m/s to 28 m/s by 1 m/s increments. At freestream velocities smaller than 4 m/s, it was difficult to obtain the needed freestream velocity stability to proceed with the measurements, due to the interference between the propeller wake and the wind tunnel s fan. At each measured freestream velocity, the propeller thrust and torque were measured along with the ambient pressure and temperature. If the torque value became too close to zero, the test was finished because the propeller was entering the windmill brake state. The collecting data procedure (see Figure 7.7) begins with the execution of a LabView data acquisition and reduction routine. The control software powers up the motor to the first predefined RPM setting and data for each freestream velocity step is collected. This procedure is repeated for all RPMs. Once the data is collected, the data reduction sub-routine is executed. The collected data was systematically reduced, recorded and stored. 122

159 Data Acquisition and Reduction Static Type of the Test? Dynamic RPM Set RPM Set No Convergence? Convergence? No Yes Yes Data Collect Speed Set No Last RPM? Convergence? No Yes Yes Data Reduction and Storing Data Collect Last Speed? No Yes Data Collect Last RPM? No Yes Data Reduction and Storing Figure 7.7 Flowchart of the test methodology. The procedure of collecting data in each freestream velocity was preceded by a data convergence check period, ensuring that the steady state was reached before start recording data. To do so, freestream and propeller rotational speed convergence criteria were implemented (see Table 7.1). Table 7.1- Convergence criteria to achieve wind tunnel steady state. Criteria Minimum time, s RPM RPM target 10 rpm 50.0 V V 0.06 m/s 50.0 target When both convergence criteria are verified, the data start to be recorded over a pre-defined period of time. Figure 7.8 shows a typical behaviour of the torque and thrust outputs during the collecting data phase, transition for the next freestream speed, convergence and, at the right, the collection of the data in the second pre-defined velocity. 123

160 Thrust Sensor Torque Sensor Collecting Data Next Freestream Speed Matching Convergence Criteria Collecting Data Figure Torque and Thrust outputs during the convergence and data collection phases Wind Tunnel Corrections Boundary corrections for propellers The interference experienced by a propeller in a closed test section of a wind tunnel was object of study by Glauert (1933). A propeller, when producing a positive thrust, creates a wake or slipstream of increased velocity as presented in Figure 7.9. Considering that the flow is confined within the test section solid walls, the condition of flow continuity leads to reduced velocity and increased pressure of the fluid surrounding the wake. These modified conditions behind the propeller change the relationship between the thrust and the freestream velocity of the wind tunnel propeller for a given rotational speed. Such that, in confined conditions, the thrust developed by the propeller is greater than would be developed in an unconstrained flow of the same freestream velocity with the same propeller rotation rate and blade pitch. Alternatively, it can also be said that the thrust developed would be equal to that which would be expected at a lower value V in the unconstrained freestream velocity. W < W W W > W Propeller Figure Effect of the propeller in a closed test section. 124

161 The correction allows the calculation of the equivalent unconstrained freestream speed at which the propeller would produce the same thrust as it is producing inside the test section. where: and V V = 1 τ 4 α τ τ 4 = T ρav α 1 = A C 7.8 where A represents the propeller disk area, C represents the jet cross sectional area and T the propeller thrust Motor fixture drag correction Due to the presence of the torque transducer and the motor fixture, the measured thrust is actually T-D fixture. To obtain the actual values of thrust, an assembly's drag model was implemented in order to correct the measured thrust values for different freestream velocities. The total force is given by: T = ρn 2 D 4 C T + D fixture 7.9 The assembly s drag was estimated according to: where: D fixture = qsc D 7.10 q = 1 2 ρv 2 drag 7.11 Considering that the fixture is located in the propeller slipstream, a fixture drag velocity was used as the corrected freestream velocity given by Glauert s method plus the slipstream induced velocity at the propeller disk given by the Actuator Disk Theory: V drag = V 2 + ( V 2 ) 2 + T 2ρA + V 7.12 Based on the characterization of drag coefficient of various 3D bodies, and according with the literature (Selig & Ananda, 2011), an approximate C D value of 1 proved to be adequate. The frontal area, was obtained from the 3D CAD model. 125

162 7.3 - Validation of the Test Rig As it was previously mentioned, the experimental setup was designed to allow the testing of a wide range of low Reynolds propellers. However, before performing any tests to new and uncatalogued propellers, the test rig measurements were validated. This validation included a sample independence test which ensures that the results are not affected by the number of samples recorded at each test point. Furthermore, the same propeller test was run in 3 different days to ensure the repeatability of the test results. To finish the validation process, the obtained data for 2 different APC propellers were compared with data obtained by UIUC (Brandt, 2005) and data collected by the propellers manufacturer APC ( APC Propeller Performance Data, 2014) Sampling time independence The stored value of any measured variable is itself the mean of N values collected at a sampling rate of 8Hz. Although a higher number of samples at each point represents a more accurate result, it also represents a higher time for data acquisition at each point. In order to find the number of samples high enough that does not affect the results without spending too much time at each test point, five different number of samples (and consequently five different times) were considered to compare the results as shown in Table 7.2. The corresponding thrust coefficient results, presented at Figure 7.10 (a), show small discrepancies between 50 samples and the remaining numbers of samples used. This discrepancy appears at an advance ratio of 0.3. For the power coefficient results (see Figure 7.10 (b)), the difference between the 2 smaller samples number (50 and 100 samples) and the remaining numbers of samples is also presented. Since the results show no significant improvements when more than 200 samples are used, it was decided to use 400 samples at each point, as a compromise between sampling number and sampling time, since with this setting each test point take less than one minute. Table 7.2- Convergence criteria to achieve wind tunnel steady state. Sampling number Sampling Time, s

163 Measurements repeatability To ensure that the measurements are not dependent on the weather conditions on a specific day, the measurements for a specific propeller were performed on 3 distinct days in terms of weather conditions. Furthermore, the measurements repeatability quality is an indicator of the integrity of the measurement system. (a) (b) (c) Figure 7.10 Number of samples independence test. (a) thrust coefficient (b) power coefficient (c) propeller efficiency. If a measurement system cannot produce consistent and repeatable measurements, a verification of the measurements accuracy cannot be performed. The test rig was submitted to 127

164 repeatability tests with the same propeller and the same test procedure. Furthermore, the same measuring instruments, with the same calibration were used. Figure 7.11 shows comparisons of the APC 11 x5.5 Thin Electric performance data collected in different days. (a) (b) (c) Figure 7.11 Three days testing. (a) thrust coefficient (b) power coefficient (c) propeller efficiency. Although the tests were performed during the summer, the weather conditions were quite different in the three days of testing, with sun on the first day moving to wind and rain on the remaining two days. As it is possible to observe in Figure 7.11, the plotted results show an exceptional repeatability for both thrust coefficient and power coefficient. In addition, since the propeller efficiency is calculated using the thrust and power coefficient it also shows good repeatability over the different days measurements. 128

165 Propeller performance data comparison To finish the validation of the test rig, the performance of two different APC commercial propellers was measured and compared with results available on the literature. The used propellers were the APC 10 x4.7 Slow Flyer and the APC 11 x5.5 Thin Electric. Their performance data were compared with UIUC measurements (Brandt et al., 2014) and with the propellers manufacturer data ( APC Propeller Performance Data, 2014). The UIUC data were downloaded from the UIUC Propeller Datasite and they were corrected according to instructions provided by Selig & Ananda (2011). The APC propeller data were obtained from the APC website ( APC Propeller Performance Data, 2014). APC 10 x4.7 Slow Flyer The APC 10 x4.7 Slow Flyer propeller (see Figure 7.12) is an injection moulded propeller. It is made from long fibre composite developed by APC ( APC Propeller Materials, 2014). Figure 7.12 APC 10 x4.7 Slow Flyer Propeller. The results of the propeller performance data for 4000 RPM are presented in Figure It is possible to observe that the UBI measured thrust coefficient values (see Figure 7.13 (a)) are slightly lower when compared to the UIUC thrust coefficient values. The values presented by the propeller s manufacturer ( APC Propeller Performance Data, 2014) shows a smaller thrust coefficient for the lowest advance ratio. In addition, the zero thrust condition occurs for higher advance ratio when compared to UBI and UIUC. Regarding the power coefficient (see Figure 7.13 (b)), the measured values show good agreement with the values presented by UIUC. The APC power coefficient values show better comparison than the thrust coefficient, although in the lower advance ratios the discrepancy tends to increase. Since the APC measurements show the zero thrust occurring at higher advance ratio, the maximum efficiency occurs at a higher advance ratio. However, the value of efficiency itself is slightly lower than the value measured by UBI and UIUC. 129

166 (a) (b) (c) Figure 7.13 APC 10 x4.7 Slow Flyer performance comparison for 4000 RPM. (a) thrust coefficient (b) power coefficient (c) propeller efficiency. Regarding the 5000 RPM results, presented in Figure 7.14, it is possible to observe that the UBI measured thrust coefficient shows good agreement with the UIUC values. The APC thrust coefficient still shows lower values for the lower advance ratios and a different slope, leading that the zero thrust condition occurs at a higher advance ratio. Regarding the power coefficient, the UBI measured values still show some offset from the UIUC values. This discrepancy is almost constant at about 6%. The APC values rapidly increase for different advance ratios lower than 0.15, maintaining a correct trend for higher advance ratios. The efficiency obtained by UBI closely matches the UIUC efficiency value and the advance ratio of its maximum. The APC efficiency is again slightly under predicted and its maximum occurs for higher advance ratios, due to the slope of the thrust coefficient values. 130

167 (a) (b) (c) Figure 7.14 APC 10x4.7 Slow Flyer performance comparison for 5000 RPM. (a) thrust coefficient (b) power coefficient (c) propeller efficiency. APC 11 x5.5 Thin Electric The APC 11 x5.5 Thin Electric propeller (see Figure 7.15) is also an injection moulded propeller using the long fibre composite as material. The performance data obtained for the APC 11 x5.5 Thin Electric propeller for 3000 RPM, 4000 RPM and 5000 RPM are presented, respectively, in Figure 7.16, Figure 7.17 and Figure

168 Figure 7.15 APC Thin Electric Propeller. For the 3000 RPM (see Figure 7.16), the thrust coefficient measured by UBI closely matches the value obtained by UIUC. The APC data keep the different behaviour presented in the APC 10 x4.7 results from the UBI and UIUC, proving that those differences are not related with the propeller shape. Concerning the power coefficient, UBI and UIUC values are in good agreement, while APC is presenting slightly higher values over the advance ratio range. As previously mentioned, the maximum efficiency, obtained by APC, occurs at a higher advance ratio due to the difference presented in the thrust coefficient measurements. Regarding the 4000 RPM (see Figure 7.17) UBI s measured thrust coefficient values are slightly higher than the values measured by UIUC, especially at lower advance ratios. The power coefficient measurements obtained by UBI are in good agreement with the measurements from UIUC. The APC measurements show a correct trend, although the values are slightly higher than those measured by UBI and UIUC. Due to the difference presented on the thrust coefficient measurements, the efficiency obtained by UBI is slightly higher than the efficiency presented by UIUC. For the 5000 RPM (see Figure 7.18) the thrust coefficient measured at UBI shows an offset when compared to the UIUC. This offset is bigger at intermediate advance ratios and tends to disappear at higher advance ratios. The APC data still presents the different behaviour previously mentioned, with lower thrust coefficient at lower advance ratios and showing the zero thrust condition at a higher advance ratio. The UBI s power coefficient values show a negative offset at lower advance ratios and a small positive offset at intermediate advance ratios. Since the differences on the thrust coefficient are bigger than the differences on power coefficient the propeller s efficiency is higher than the efficiency obtained by UIUC. 132

169 (a) (b) (c) Figure APC 11 x5.5 Thin Electric performance comparison for 3000 RPM. (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 133

170 (a) (b) (c) Figure APC 11 x5.5 Thin Electric performance comparison for 4000 RPM. (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 134

171 (a) (b) (c) Figure APC 11 x5.5 Thin Electric performance comparison for 5000 RPM. (a) thrust coefficient (b) power coefficient (c) propeller efficiency. Observing all the rotational speeds, it is possible to conclude that the thrust coefficient increases with the increase in the propeller rotational speed for the same advance ratio. The increase in the rotational speed leads to an increment in the Reynolds number at which the airfoil is operating. Since these low Reynolds propellers operate around their airfoil's critical Reynolds numbers, this increase of the rotational speed consequently leads to an increment in the airfoils maximum lift coefficient, causing an increment in the thrust coefficient. In addition, the lift-to-drag ratio also increases with the Reynolds number increment leading to higher efficiencies at higher rotational speeds. 135

172 Uncertainty Analysis To calculate the level of precision of the obtained results an uncertainty analysis was performed. The error propagation begins with the primary measured quantities including thrust, torque, atmospheric pressure, flow s temperature and flow differential pressure. During this analysis it was assumed that there is no error on the conversion from the sensor s voltages to the physical quantities. In addition it was considered that the propeller s diameter was exact as specified by the manufacturer. To start the analysis each sensor uncertainty was considered as presented at Table 7.3. Table 7.3- Convergence criteria to achieve wind tunnel steady state. Measurement Sensor Uncertainty Thrust FGP FN3148 ± 0.05 N Torque Transducer Techniques RTS-100 ± N.m Atmospheric ± 1.0 K National Instruments LM335 Temperature Atmospheric ±30 Pa Freescale Semiconductor MPXA4115A Pressure Propeller RPM Fairchild Semiconductor QRD1114 ± 5 RPM Differential Pressure MKS 226A Differential Pressure Manometer ± (0.3 x Reading) Pa The error on the freestream velocity is given by: V σ V = [ (p 1 p 2 ) δ(p 1 p 2 )] 2 + [ V 2 δt T atm ] + [ V 2 δp atm P atm ] atm 7.13 The error on advance ratio can be expressed by: J σ J = [ (p 1 p 2 ) δ(p 1 p 2 )] 2 J + [ δt T atm ] atm 2 J + [ δp P atm ] atm 2 + [ J n δn] The error on C T is given by: σ CT = [ C 2 T T δt] + [ C 2 T δt T atm ] + [ C 2 T δp atm P atm ] + [ C 2 T atm n δn] 7.15 The error on C P is given by: σ CP = [ C 2 P Q δq] + [ C 2 P δt T atm ] + [ C 2 P δp atm P atm ] + [ C 2 P atm n δn]

173 And finally the error on efficiency is as follow: σ η = [ η 2 T δt] + [ η 2 Q δq] + [ η 2 δt T atm ] + [ η 2 δp atm P atm ] + [ η 2 atm n δn] + 2 V + [ (p 1 p 2 ) δ(p 1 p 2 )] 7.17 A summary of the uncertainty analysis relative to the APC 10 x7 Slow Flyer propeller (see Section 7.4) at 5000 RPM test is presented at Figure 7.3. Table 7.4- APC 10 x7 Slow Flyer propeller uncertainty for 4000 RPM. Uncertainty V V, % J, % C t, % C p, % η, % It can be noted that for freestream velocities around 5-6 m/s interval there is an increased uncertainty in the results. By analysing the raw data, this appears to be a result of higher fluctuations on the measurements around this velocity interval. Observing the Table 7.4 it is possible to conclude that for freestream velocities above 7 m/s, the uncertainty in this parameter is less than 1%. The uncertainty in C t is typically less than 0.3% while the uncertainty in C P is typically less than 0.6%. Additionally, the uncertainty in η is typically less than 1%. The observed uncertainties proved to be small and, as expected, they increase as the predominant primary measurement decreases such as the uncertainty in freestream velocity which increases as P diff measurements decrease. This increased uncertainty can be found at the 5-6 m/s freestream velocity interval for all the tests. 137

174 7.4 - APC 10 x7 SF Propeller Inverse Design Propeller CAD inverse design An APC 10 x7 SF original propeller was cutted and digitized as presented by Carvalho (2013), following the indiactions given in Drela (2005a). The resulting airfoil was imported in the CAD Software and the propeller was designed and manufactured in order to be tested in the UBI s wind tunnel and compared with the original APC 10 x7 SF propeller. The coordinates of the airfoils were exported from JBLADE and imported into CATIA V5 using a Microsoft Excel macro. The airfoils were radially positioned using their leading edge as the origin (see Figure 7.19 (a)). Subsequently, the airfoils were translated in the chord wise direction up to their quarter chord positions became coincident with the radial axis (see Figure 7.19 (b)). This represents the geometry as it is considered inside JBLADE, since the JBLADE software does not account any sweep in the blades. The airfoils were then independently rotated about their quarter chord point, according to the blade incidence distribution in the geometry data obtained in the literature (Brandt et al., 2014). (a) (b) (c) Figure 7.19 Propeller CAD design steps (a) airfoils import and leading edge alignment (b) airfoils translation to their quarter chord point (c) airfoils pitch setting. The leading and trailing edges guidelines were built passing on each airfoil section and the CATIA multi-section solid tool was used to obtain the propeller blade. The hub region was then designed and attached to the blades, resulting in the propeller presented in Figure Figure Top view of final blade geometry. 138

175 Moulds manufacture In order to perfectly replicate the geometry, it was decided to use CNC machined moulds. To design the moulds, the top and bottom surfaces of the blade were extracted and 2 different solid parts were obtained in CATIA (see Figure 7.21). After obtaining the two mould halves, four holes were added to ensure the correct alignment during the mould filling. Each mould geometry was then exported and imported in the milling CAM software, allowing the generation of the three axis CNC Router cutter paths. Figure 7.21 View of the blade within the mould, showing the mould halves matching. The PowerMill CAM software was used to generate the necessary G code. After importing the geometry into the software the dimensions of the raw material block were defined. The next step was the definition of different tools used along the machining process. (a) (b) Figure 7.22 (a) Illustration of the mould after the roughing path. (b) )Illustration of the mould after the finishing path. The 8 mm drill was firstly used to remove the bigger part of the material (see Figure 7.22 (a)) while the 3 mm drill was used to finish the surface of the mould (see Figure 7.22 (b)). The final obtained mould is presented in Figure

176 Figure 7.23 Final obtained mould. While being machined, the moulds were supported at various locations with two face adhesive tape to prevent any movement of the block due to the cutting forces applied by CNC machine Propeller manufacture The material used to manufacture the propeller was epoxy resin reinforced with carbon fibre. The different layers of carbon fibre were previously cutted to correctly fit inside the mould. Four layers were used to give the necessary thickness to the propeller blades, with some extra reinforcements in the root region as presented in Figure Figure 7.24 Carbon fibre placement inside the moulds. The carbon fibre was then impregnated with epoxy resin and fitted within the moulds. After inserting the impregnated carbon fibre cloth layers, the moulds were closed and filled with epoxy in order to fill any air bubbles and give the correct blade shape to the propeller s blades (see Figure 7.25). Figure 7.25 Closed moulds with carbon fibre inside and with a hole to allow the moulds fill with epoxy resin. 140

177 After the epoxy curing process the moulds were opened and the blades were finally handfinished to achieve a smooth surface. The final produced propeller is presented in Figure Figure 7.26 Final manufactured propeller, representing the APC 10 x7 SF propeller in JBLADE Software. The manufactured propeller was then mounted in the experimental test rig presented in Section 7.1 and it was tested. Its performance is presented in Section Results and Discussion The replica of APC 10 x7 Slow Flyer was tested in the wind tunnel and the data was compared with JBLADE predictions. Figure 7.27 presents the static thrust and torque obtained in UBI s wind tunnel for the original APC 10 x7 SF and for the built propeller replica. (a) (b) Figure APC 10 x7 Slow Flyer static performance comparison with JBLADE predictions. (a) propeller thrust (b) propeller torque Observing Figure 7.27 (a) it is possible to observe that the JBLADE predictions are overestimating the thrust coefficient, when compared to the APC 10 x7 SF replica but are close to the original propeller performance. Regarding the torque (see Figure 7.27 (b)) the JBLADE is also overestimating the torque when compared with replicated propeller. However, 141

178 the predictions for higher rotational speeds tend to approach the replicated propeller data. Again, the predictions are quite close to the original propeller data although deteriorate towards higher advance ratios. Figure 7.28 presents the propeller wind tunnel measurements and JBLADE predictions for 3000 RPM. It is possible to observe that the thrust coefficient (see Figure 7.28 (a)) of the original propeller is higher than the replica built at UBI and also higher than JBLADE predictions. It is also possible to observe a slightly bigger thrust coefficient predicted by JBLADE when compared to the UIUC data. For bigger advance ratios, when the Reynolds numbers become bigger (but still in the 10 5 range), the predictions of the JBLADE match the replicated propeller experimental data. (a) (b) (c) Figure APC 10 x7 Slow Flyer performance comparison with JBLADE Predictions for 3000 RPM (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 142

179 Observing the power coefficient (see Figure 7.28 (b)) it is possible to conclude that the power coefficient of the original propeller obtained in UBI s wind tunnel is bigger than that of the UIUC data. The power coefficient obtained for the APC 10 x7 SF replicated at UBI is also smaller, following the thrust coefficient results. JBLADE power coefficient predictions also match the replicated propeller measurements at bigger advance ratios. Since the propeller efficiency is directly dependent on the thrust and power coefficient, the measurements obtained at UBI s wind tunnel indicate higher maximum efficiency, occurring at bigger advance ratio for the original APC 10 x7 SF propeller. Regarding the replicated propeller measurements, UIUC measurements and JBLADE predictions, they indicate similar maximum efficiency value, occurring for an advance ratio of about 0.5. The propellers measurements for 6000 RPM are presented in Figure Observing the thrust coefficient measurements (see Figure 7.29 (a)) it is possible to observe the same trend that was presented in the 3000 RPM measurements, with the original propeller presenting bigger thrust coefficient. JBLADE is still overestimating the propeller thrust coefficient for smaller advance ratios but as the Reynolds numbers increase, the prediction gets closer to the measurements. Regarding power coefficient (see Figure 7.29 (b)), the original propeller data obtained in the UBI s wind tunnel is also presenting higher power coefficient when compared with UIUC measurements and with the replicated propeller. JBLADE is still overestimating the power coefficient for small advance ratios. However, contrary to the 3000 RPM results, for 6000 RPM is underestimating the power coefficient at bigger advance ratios. Observing the propeller efficiency (see Figure 7.29 (c)) it is possible to conclude that JBLADE is predicting a similar maximum efficiency value as the replicated propeller. However, JBLADE is predicting the maximum efficiency for bigger advance ratio than the experimental measurements. Following what was presented for the 3000 RPM, the original propeller measurements at UBI are indicating a bigger maximum efficiency value, occurring at bigger advance ratio, when compared to the UIUC and replicated propeller measurements. Generally, the results presented in Figure 7.27, Figure 7.28 and Figure 7.29 show good agreement between JBLADE and measurements. Thus, it was shown that JBLADE can be used to accurately predict the propeller performance. From the general comparison of the original propeller and its replica it can be concluded that large discrepancies exist between them. This can be due to the method suggested by Drela, (2005a) for obtaining the airfoils geometry and blade pitch and chord distributions. A 3D scan for obtaining the replica would probably result in a closer replica. On the other hand, the significant discrepancies between the replica experimental data and the JBLADE predictions 143

180 suggest that the structural analysis sub-module should interact with the aerodynamic simulation sub-module to account the fluid-structure interaction on the propeller performance predictions. For now, the JBLADE structure sub-module can only be used in the perspective of correcting the working propeller geometry due to loads on the fabrication of the blades as the literature sometimes mentions as hot vs cold propeller shapes. (a) (b) (c) Figure APC 10 x7 Slow Flyer performance comparison with propeller built for a rotational speed of 6000 RPM (a) thrust coefficient (b) power coefficient (c) propeller efficiency. 144

181 Chapter 8 Conclusions Summary and conclusions The JBLADE software was developed and validated through the comparison of different propellers performance data from RANS CFD and experiments. It was found that the correct modelling of the post-stall airfoil characteristics play a major role, especially in the low advance-ratio performance predictions. A new 3D equilibrium model was developed and validated against conventional RANS CFD simulations. A new correlation for predicting the drag coefficient at 90º angle of attack was developed allowing an improved modelling of the airfoil post stall characteristics that proved to be reliable and improves the performance predictions. The fitting of the correlation originally suggested by Timmer (2010) was also improved and implemented. Different post-stall models originally developed for wind turbines were extended to propeller performance predictions showing that they can improve the predictions over other available codes. The Inverse Design sub-module was integrated in the JBLADE software and validated against reference data. A basic Structural sub-module was also implemented and validated against FEM Software data. The results have shown that both the tip displacement and the torsion along the blade predicted by JBLADE are in good agreement with the more complex CATIA V5 FEM simulations. In addition, this sub-module allows the prediction of propeller s deflections due to the thrust generation for a given operation point leading to an extra optimization loop, in which the user can re-design the propeller to achieve its maximum efficiency when operating, instead of optimize only the cold geometry. It should be mentioned that although throughout the validation significant discrepancies were observed between JBLADE and the experimental data, those propellers geometries always corresponded to the cold geometry while the experimental performance data occurs in the hot geometry. So, one could not expect excellent fits. For now, the JBLADE structure sub-module can only be used in the perspective of correcting the working propeller geometry due to loads on the fabrication of the blades as the literature sometimes mentions as hot vs cold propeller 145

182 shapes. It was shown that the XFOIL remains an excellent airfoil design and analysis tool with predictions being comparable to those of RANS CFD with the most suited turbulence and transition closure models. A new airfoil to use in the MAAT cruiser airship propeller was developed. It was shown that a new concept of using the L 3/2 /D optimization in the blade leads to more efficient propellers. The APC 10 x7 SF propeller experimental data was used to validate JBLADE for low Reynolds number simulations. A new low Reynolds propellers wind tunnel test rig was developed and validated through the comparison of the performance with reference data available in the literature for some commercially available propellers. The new test rig proved to be suitable to test a wide range of low Reynolds number propellers up to a diameter of about 14. Furthermore, a replica of APC 10 x7 SF was built to test a prototype construction technique and its performance was characterized in the wind tunnel. Considering the work presented in this thesis, the major conclusions are: A new software suitable for low Reynolds propeller design was developed and validated against numerical and experimental data. An inverse design methodology together with a simple structural sub-module were implemented in the JBLADE and validated. A new 3D Equilibrium model was developed and validated. A new method to calculate the drag coefficient of the airfoils at 90 degrees, based on the airfoil s leading edge shape was developed. The post stall models were extended to propeller performance prediction and they were implemented and validated in the JBLADE Software. An efficient airfoil to use at high altitudes in low Reynolds propellers was developed. Two propellers, for application on the MAAT cruiser airship were designed, proving that a new concept of using the airfoil best L 3/2 /D produces more efficient propellers. An original experimental test rig was developed and validated against reference data. A replica of an APC 10 x7 SF propeller was built and tested. 146

183 8.2 - Future Works Regarding future works, it is proposed to develop a more complete 3D equilibrium model that will not be dependent of the constant axial induction assumption on the propeller s disk. In the future, the JBLADE propeller structure sub-module can be used to interact with the aerodynamic simulation sub-module to account the fluid-structure interaction on the propeller performance predictions. Some additional sub-modules can be implemented in JBLADE such as an electrical motor model, to couple with the existing aerodynamic module, in order to estimate the efficiency of the complete powerplant, instead of the propeller performance alone. It can also be implemented the possibility to account for the blade sweep of the propellers. Other propeller blades structure concepts can be implemented in the structural module and the formulation itself can be improved. 147

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191 Silva, D., Avelino, M. & De-Lemos, M. (2002). Numerical study of the airflow around the airfoil S1223. In II Congresso Nacional de Engenharia Mecânica. João Pessoa. Snel, H., Houwink, R. & Bosschers, J. (1994). Sectional Prediction of Lift Coefficients on Rotating Wind Turbine Blades in Stall. Petten. Sommers, D. & Maughmer, M. (2003). Theoretical Aerodynamic Analyses of Six Airfoils for Use on Small Wind Turbines. Golden. Strash, D., Lednicer, D. & Rubin, T. (1998). Analysis of propeller-induced aerodynamic effects. In 16th AIAA Applied Aerodynamics Conference. doi: / Taylor, G. (1939). Some recent developments in the study of turbulence. In Fifth International Congress for Applied Mechanics. Cambridge, Massachusetts. Theodorsen, T. (1948). Theory of Propellers. New York: McGraw-Hill Book Company. Theodorsen, T., Stickle, G. W. & Brevoort, M. J. (1937). Caracteristics of Six Propellers Including the High-Speed Range - NACA TR No Langley. Thole, K. & Bogard, D. (1996). High freestream turbulence effects on turbulent boundary layers. Journal of Fluids Engineering Vol.118, pp Timmer, W. A. (2010). Aerodynamic characteristics of wind turbine blade airfoils at high angles-of-attack. In TORQUE 2010: The Science of Making Torque from Wind, pp Creete. Viterna, L. A. & Janetzke, D. C. (1982). Theoretical and experimental power from large horizontal-axis wind turbines. Washington, DC (United States). doi: / Viterna, L. & Corrigan, R. (1982). Fixed Pitch Rotor Performance of Large Horizontal Axis Wind Turbines. Cleveland. Vizinho, R., Pascoa, J. C. & Silvestre, M. (2013). High Altitude Transitional Flow Computation for a Propulsion System Nacelle of MAAT Airship. SAE International Journal of Aerospace Vol.6, (2), pp doi: / Volino, R. J. (1998). A New Model for Free-Stream Turbulence Effects on Boundary Layers. Journal of Turbomachinery Vol.120, pp Wald, Q. R. (2006). The aerodynamics of propellers. Progress in Aerospace Sciences Vol.42, (2), pp doi: /j.paerosci Walters, D. K. & Cokljat, D. (2008). A Three-Equation Eddy-Viscosity Model for Reynolds- Averaged Navier Stokes Simulations of Transitional Flow. Journal of Fluids Engineering Vol.130, (12), pp doi: / Walters, D. K. & Leylek, J. H. (2004). A New Model for Boundary Layer Transition Using a Single-Point RANS Approach. Journal of Turbomachinery Vol.126, (1), pp doi: / Wang, X., Ma, Y. & Shan, X. (2009). Modeling of Stratosphere Airship. In Advances in Theoretical and Applied Mechanics, pp Welty, G. D. (1935). Light Alloy Propeller Blades. Journal of the Aeronautical Sciences Vol.2, (1), pp doi: /

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193 Appendix A Partial Derivatives for Error Estimation 157

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195 A.1 Freestream Velocity W (p 1 p 2 ) = W T atm = W P atm = 625 R T atm 609 P atm 1250(p 1 p 2 )RT atm 609 P atm 625 R (p 1 p 2 ) 609 P atm 1250(p 1 p 2 )RT atm 609 P atm 625(p 1 p 2 ) R T atm P atm 1250(p 1 p 2 )RT atm 609 P atm A.1 A.2 A.3 A.2 Advance Ratio J (p 1 p 2 ) = J T atm = J P atm = 625 R T atm 609D P atm n 1250(p 1 p 2 )RT atm 609 P atm 625 R (p 1 p 2 ) 609 P atm 1250(p 1 p 2 )RT atm 609 P atm 625(p 1 p 2 ) R T atm DP atm n 1250(p 1 p 2 )RT atm 609 P atm 1250(p J 1 p 2 )RT atm n = 609 P atm Dn 2 A.4 A.5 A.6 A.7 A.3 Thrust Coefficient C t T = R T atm A.8 D 4 P atm n 2 C t R T A.9 = T atm D 4 P atm n 2 C t = R T atmt A.10 P atm D 4 2 P atm n 2 C t n = 2R T atmt D 4 P atm n 3 A

196 A.4 Power Coefficient C p Q = 2πRT atm D 5 P atm n 2 A.12 C p = 2πRQ A.13 T atm D 5 P atm n 2 C p = 2πRT atmq A.14 P atm D 5 2 P atm n 2 C p n = 4πRT atmq D 5 P atm n 3 A.15 A.5 Propeller Efficiency η (p 1 p 2 ) = η T atm = 1250(p η 1 p 2 )RT atm T = 609 P atm 2πQn 1250(p η T 1 p 2 )RT atm Q = 609 P atm 2πQ 2 n 625 R T atm T 1218πP atm Qn 1250(p 1 p 2 )RT atm 609 P atm 625 R(p 1 p 2 )T 1218πP atm Qn 1250(p 1 p 2 )RT atm 609 P atm η 625 RP atm (p 1 p 2 )T = P atm πP atm Qn 1250(p 1 p 2 )RT atm 609 P atm 1250(p η T 1 p 2 )RT atm n = 609 P atm 2πQn 2 A.16 A.17 A.18 A.19 A.20 A

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199 List of Publications Peer Reviewed Journal Papers I. Validations of New Formulations for Propeller Analysis Morgado, J., Silvestre, M. A. R. and Páscoa, J. C. Journal of Propulsion and Power, Vol 31 (2015) pp II. Propeller Performance Measurements at Low Reynolds Numbers Silvestre, M. A. R., Morgado, J., Alves, P., Santos, P., Gamboa, P. and Páscoa, J. C. International Journal of Mechanics Vol. 9 (2015) pp ISSN: III. A Comparison of Post-Stall Models Extended for Propeller Performance Prediction Morgado, J., Silvestre, M. A. R. and Páscoa, J. C. Accepted for Publication, Aircraft Engineering and Aerospace Technology, 2015 DOI: /AEAT R1. IV. High Propeller Design and Analysis Morgado, J.,Abdollahzadeh, M., Silvestre, M. A. R. and Páscoa, J. C. Aerospace Science and Technology, Vol. 45 (2015) pp V. Comparison between CFD and XFOIL Predictions for High Lift, Low Reynolds Number Airfoils Morgado, J., Vizinho, R., Silvestre, M. A. R. and Páscoa, J. C. Aerospace Science and Technology, Vol. 52 (2016) pp

200 Peer Reviewed International Conferences I. Full Range Airfoil Polars for Propeller Blade Element Momentum Analysis Morgado, J., Silvestre, M. A. R. and Páscoa, J. C. Proc. of 2013 International Powered Lift Conference, AIAA, Los Angeles, USA, August II. JBLADE: a Propeller Design and Analysis Code Silvestre, M. A. R., Morgado, J. and Páscoa, J. C. Proc. of 2013 International Powered Lift Conference, AIAA, Los Angeles, USA, August III. A new Software for Propeller Design and Analysis Morgado, J., Silvestre, M. A. R. and Páscoa, J. C. 6th AFCEA Students Conference, AFCEA, Bucharest, Romania, March IV. Comparison between CFD and XFOIL Predictions for High Lift, Low Reynolds Number Airfoils Morgado, J., Vizinho, R., Silvestre, M. A. R. and Páscoa, J. C. ESCO 2014, 4th European Seminar on Computing, Pilsen, Czech Republic, June, V. Low Reynolds Propeller Performance Testing Silvestre, M. A. R., Morgado, J., Alves, P., Santos, P., Gamboa, P. and Páscoa, J. C. 5th International Conference on FLuid Mechanics and Heat & Mass Transfer, WSEAS, Lisbon, Portugal, October Peer Reviewed National Conferences I. Parametric Study of a High Altitude Airship According to the Multi-Body Concept for Advanced Airship Transport - MAAT Morgado, J., Silvestre, M. A. R. and Páscoa, J. C. Proc. of IV Conferência Nacional Em Mecânica Dos Fluidos, Termodinâmica e Energia, LNEC, Lisbon, Portugal, May

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213 B.II Propeller Performance Measurements at Low Reynolds Numbers 177

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227 B.III A Comparison of Post-Stall Models Extended for Propeller Performance Prediction 191

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241 B.IV High altitude propeller design and analysis 205

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251 B.V XFOIL vs CFD performance predictions for high lift low Reynolds number airfoils 215

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